Of course, the nature of such a list is a bit out of the ordinary for me, since I don't typically like to tell people what to do. For this reason I'll try to not say anything too horrendously offensive about your mothers or talent choices. Let's get on with it then, shall we?
Play to your strengths The internet is a great place to complain about everything, and the shortcomings of the priest class are definitely a discussion that comes up frequently here. But whether you agree or disagree with me (or anyone) about how priests are now (or ever), you should always remember to play to your strengths. That means looking at your best spells (Power Word: Shield, Penance, Circle of Healing, Empowered Renew right now, for exampe) and finding ways to apply them to what you're doing. If you're a Renew-centric holy priest, for example, don't try to convince your 10-man raid that you should be keeping up the tanks. Hit the raid up instead, and let the druid try her hand at single target heals. (Druids can do more than HoTs, contrary to popular belief. They're exceptional healers, some of them just get grumpy about casting Nourish.)
Basically, what this comes down to is your ability to adapt, which is actually good advice to all healers. As this game changes and evolves, so will your strengths and weaknesses. As a priest, you will see many ups and downs and you should always be willing to try out new styles of healing to account for the shifts.
Cancel casts This topic especially is one I've wanted to discuss for a while but knew I'd never be able to turn into a full feature. Canceling casts is when you stop casting a spell you were casting by moving, jumping, or using a stop casting macro. Some might say canceling casts goes against Penance Priest's ABC (always be casting) advice, which I advocate, but I personally advise for the use of cancel casting for efficiency. Sure, mana isn't an issue now (though yes, it will be an issue later) but even still, canceling a bad cast will save you time if you're quick about it; saving time means saving lives.
Assuming you're canceling a cast spell (as opposed to a channel spell) you will immediately reset the global cooldown which was in process, leaving you free to cast something else. (For this reason, I do not recommend you jump to cancel a cast, as you will have to wait to land before you can begin casting again.) In addition to resetting your GCD, you will not consume any mana until your cast is finished, so there isn't any penalty for doing it.
The primary reason to cancel a cast is if it was a bad cast. Say you are about to heal a party member and before your heal is finished, you see that another healer has already taken care of that damage and healed the player to full. Finishing the cast now would result in overhealing, which is a waste of mana and time. So, instead of following through with your heal, cancel it and move on to your next target. The possible exception to this is for tank healing, where the tank is being hit continuously by a boss or add, and incoming damage could occur as your heal is finishing. In that case, go ahead and follow through with all your casts.
Oh, and if you're not sure whether that player is going to take more damage or not, go ahead and follow through then as well.
Anticipate damage You'd be surprised how many healers don't bother to look outside their party and raid frames. The frames sure are convenient, but sometimes they get us focused on the wrong place. You may remember this vaguely from leveling up: incoming damage is often portrayed in the game world through particular animations of the NPC models. Damage will frequently follow an attack animation. If you take the time to watch NPC models you'll be able to get a better understanding of what animations mean what (sometimes they'll all share the same animation, but sometimes they'll be customized.) By being able to spot the moment before damage occurs, you'll be able to time your heals better. This is especially valuable for holy priests who want to use Prayer of Healing.
Setting your focus frame to the portrait of the boss will help you out further, by allowing you to see the cast bar of the boss.
Heal pets You can blame Frostheim for this one. In honesty though, you can and should heal pets, just make sure that you're not ignoring any of your other duties before you do. All other members of the raid (except that terrible DPS warrior who just ran off the side of the Frozen Throne) get healing priority over pets. However, that doesn't mean you can't toss pet heals or a dispel when you have the GCD to spare. Pets are another member of the raid, and the death of one can equate to a DPS loss.
Use Dispel Magic As well as Mass Dispel and Abolish Disease! As a healer you may think your job is just to heal, but remember that dispelling is part of healing. A fast dispel can sometimes even save your target from any damage that the magical or disease debuff would have inflicted. You should keep your dispel key bindings close to your healing spells and try to treat every debuff as quickly as possible, just like you would treat damage with heals. There are obvious exceptions: you don't want to dispel Unstable Affliction and you don't need to dispel at such a hurried pace for less threatening debuffs.
Utilize your mobility A strength of the priest in either spec is high mobility. Holy and discipline priests tout an impressive list of instant cast spells, and a few other bells and whistles to help. When other classes are moving and direct heals might be sparse, cash in by firing off your quick heals. A priest who understand this is a huge asset to his or her raid team by keeping players up through transitions in a fight. A wipe might be the result of a paladin not keeping up a tank during a movement phase, but you're all in it together and you should try to help out where you can (while simultaneously jabbing the paladin with snarky remarks.)
Communicate your cooldown usage This means Pain Suppression, Power Infusion, Guardian Spirit, Hymn of Hope, and Divine Hymn. This is an obvious one, and I know I've mentioned it in passing before, but I always want to stress it more. Communication is one of the biggest weaknesses of every fledgling priest, especially since we have so many abilities that can benefit the party or raid. A good player communicates what he does so the raid knows when it can and shouldn't relax, and helps us all not step on each others' toes as well.
Heal yourself We have Binding Heal for a reason, use it! Another healer should rarely need to worry about your health to the point that you require a direct heal from her. Heals cost time, and since it's so easy for you to do your job and heal yourself simultaneously, there are no excuses for why you shouldn't be at full health 90% of the time.
Bind your buffs You don't want your buffs falling off while in combat, so it's a good idea to bind your buffs somewhere on your keyboard so you can easily reapply them when they expire, are dispelled, or disappear due to player death. When players require buffs it's much easier to hit a binding then go clicking off somewhere on the far reaches of your screen. Re-application of short or charge buffs like Fear Ward and Inner Fire are perfect for binding, and once Inner Will shows up in Cataclysm, you might be wanting to switch between buffs quite quickly. Practicing now would be a good preparation.
Prioritize regen when your gear is bad At low levels and when you first hit 80, mana is going to be what holds you back. To keep up with your party (or better geared players) you'll want to have as much regeneration as you can to stay operational in fights. Gear with your regen stat of choice, plus trinkets, gems, flasks and buff food will help you endure each encounter until your gear eventually fills in the gaps.
Use the Glyph of Guardian Spirit Don't give me that look, you non-believers. Okay, okay, listen up. Or read up ... whatever. The Glyph of Guardian Spirit is an ideal choice for raiding in 10 or 25-man. This glyph isn't helping you every second, but having it will allow you more control and freedom over your usage of Guardian Spirit. Guardian Spirit is a very strong ability, but without the glyph it suffers from a long cooldown. Cooldowns like this often result in the hoarding of abilities and force players to wait for the perfect moment in a fight to use their spells. Problem is, that moment can sometimes never come. By lowering the cooldown, you''ll find you can use Guardian Spirit more readily, and in doing so, be able to save the day more often (After thought: or rather, try to save the day more often, since if your Guardian Spirit does actually get consumed, it will be on the normal cooldown. The glyph forgives using it "just in case," and that is still a very good thing.)
Refuse to explore your other healing spec Basically, don't be a holy priests who trash talks discipline as an inferior spec without ever trying it out for yourself. Likewise, don't be a discipline priest who thinks holy is a stuffy, old codger of a spec. If you enjoy healing you should be able to appreciate the strengths of each one, if you try them. I used to detest holy because all I saw were a bunch of nose-in-the-air holy priests who couldn't even match their actions to their words. When I started to try out holy for myself and really get a feel for it, I found potential in it that all the priests I had known before never showed me. Nowadays, I wish I could play holy more.
Hold onto regen like a childhood keepsake When you're struggling to get quality gear, then like I said before, go ahead and prioritize regen. On the other hand, if you're catching up on your gear and have a nice healer trinket or two, why not try skipping some intellect gems or spirit gear in favor of spellpower or haste? I say this again and again, but really consider how much mana you have at the end of an average fight and if you have quite a bit, you can probably cut back on regen stats. Push yourself, and your gameplay to see what you're capable of with less.
Be one of those disc priests You know the ones, the ones who excuse their own poor performance as healers on a lack of absorbs tracking. I know I have said meters aren't important, but I mean that in the sense that you shouldn't use them to beat players of other classes and specs. They are still a solid tool to use for self-assessment.
Now yes, your healing will be lower compared to your absorbs, but don't make your fellow disc brothers and sisters look bad by failing to look at yourself objectively. A lot of disc's bad reputation comes from ignorance of other players, but there are plenty of disc priests out there who make things worse by stubbornly insisting their performance is up to par when it isn't. Be proactive; download Skada or RecountGuessedAbsorbs and monitor both your healing output, and your absorb output. (Weren't you already doing this to link to the jerks in PUGs?) Compare your numbers on Skada to other discipline priests you know, or even some of the players listed on leader boards at World of Logs; see how close or far you are to them. Don't think it's fair to compare yourself to better geared players? Okay, figure out what the average item level of your gear is and then compare yourself to disc priests from previous tiers of content with similar gear. You don't have to do as much healing as these players, but you should push yourself to try and get closer to their numbers.
Underestimate the strength of some spells Spells like Prayer of Mending, for example, can do more effective healing than any other spell you actively use just by randomly bouncing around. That's rather significant for something you "fire and forget." Holy Nova is another example of a spell that actually has some respectable fire power (for both heals and damage) but most players ignore it in favor of bigger, more familiar spells. Remember that prior to Wrath, Holy Nova was a talented spell only, which means some players went for ages without having it or using it. Now that it's baseline, you should explore it and other spells like it more!
Forget to look at your mana bar You don't ever want to be surprised that you've gone OOM. If you keep an eye out on your mana, you'll be able to strategically plan your Hymn of Hope and Shadowfiend usage, so that you're never running up against a tricky spot in the encounter while running on empty. If you have trouble watching your mana, set up Power Auras, or an advanced combat text addon (like MikScrollingBattleText) to scream at you when you're a 30% mana (or whatever percentage you want to set it to.)
Cast Prayer of Healing needlessly I frequently say that Prayer of Healing is a situational spell, but now I am going to finally explain why I feel this way a bit more. In a 5-man, Prayer of Healing is great, but in a raid it's usually not. Think about when you have a scenario where an entire group in your raid needs direct healing. To me, those situations are rare, and for most of them, by the time you've got Prayer of Healing cast, other members of your raid have picked up the heals on most of the group you had targeted. That means by the time your Prayer of Healing is cast, you're only healing one or two raid members (and likely just topping them off) and the rest is overheal. This is a huge waste, and kind of lazy since most of the time you'd be better off hitting a few people with some single-target Renews, or a Flash Heal. Only in situations where you can anticipate group wide damage, or when you're trying to make up for a dead (or terrible) healer, does Prayer of Healing really start to come through as an optimal choice.
So that's it, now I can cross off all those drifting ideas in my notebook. Unless of course you all think there is anything in here that needs more attention. If you have any questions, your own "do's and don't's," or just want to argue out something with me, feel free to leave a comment and get a discussion started.
Want to find more great tips for carrying out your priestly duties? Spiritual Guidance has you covered with all there is to know. Check out Holy 101 or Disc 101 for an introduction to healing as a priest, or for the party-minded healer, check out a priest's guide to tanks.