The way Spell Power works is that all +Damage and all +Healing are collapsed into one stat: Spell Power. Healing spells were rumored to just use 2x your Spell Power as its base, but that isn't really the case. Healing spells just generally use a higher coefficient than damaging spells. Say, Flash of Light will get a greater benefit than Scorch, both being spells with a 1.5 second cast time. There was a lot of worry that this change would gut some classes' healing numbers due to the transition over to the new system, but the consensus has actually been that most classes are putting out bigger healing numbers for one reason or another. Probably the coefficients are balanced in a way that they will have very little change (if any) and the higher numbers we're seeing are a result of things like Blessing of Light being folded into the base healing of Paladin heals.
In the short term, when we're looking at soloing and leveling, this has done some nice things. I won't post spreadsheets and charts displaying the DPS changes and things like that, but I can say that soloing in your healing gear has gotten much, much easier. It isn't ideal DPS gear, but it has become passable, much moreso than it was. At the same time, your DPS gear has become passable Healing gear, though again not ideal.
Now, my situation is not going to be identical to everyone's since my DPS gear is largely from Sunwell Plateau, but I disenchanted my mostly T6 Healing gear shortly after logging my Priest onto the beta realms, because my DPS gear was basically just as good for healing 5-man dungeons. There was no reason to have two sets. It functions just fine both as Healing gear and DPS gear. It wasn't ideal for both roles, but it was more than enough. In my damage gear and specced Holy, I still managed to crit a Greater Heal for nearly 13,000, because all of the Spell Damage I used to have is now working at a coefficient equal to if it were +Healing. Of course, +Healing isn't the only stat you need as a Healer, but the point is my damage gear doubled as Healing gear just fine.
Another thing this has done is provide options. For example, a quest that takes place in the Nexus offers Mantle of Keristrasza or Cloak of Azure Lights. Both cloaks can be used by certain classes for certain specs, not just healing and not just DPS. There isn't just one DPS cloak and one Healing cloak. One of them is probably better suited to your spec, but the other may be better suited to your personal playstyle. That's fine. You have more choices available to you now.
Does this choice mean more casters and healers will make poor gear choices and roll on things they probably shouldn't in dungeons? Well... yeah, unfortunately. Anytime you give people choices many of them will make the wrong ones. However, overall, I think it's turning out to be a pretty good thing, especially for healers. My Shaman in Karazhan gear managed to solo through the newbie zones of Northrend specced Ele in Resto gear without any hitches. When I upgraded pieces of gear, I didn't need to worry whether or not I needed to save what I replaced for X spec of Y situation. I vendored it and moved on with life.
In the long term this choice will, as always, disintegrate a little bit come raiding. Only if you raid hardcore, though. Hardcore is another nebulous term, but let's pretend we're on the same page, eh? In a 'hardcore' progression guild, there's always going to be a gearset that is ideal for your spec. That's just the nature of gaming. Perfection. The freedom that Spell Power gives you in choosing your gear will largely fade away. But you know, that's fine. It's no big deal, really. It's still a huge boon to Healers and Casters alike, especially the ones of the Hybrid variety.
Oh, you Melee DPS guys? You guys with AP to Spell Power talents? It's not just your Shocks and Judgements that are getting a fun little boost, no sir. My Ret Paladin is having quite a lot of fun owning face and then healing herself up with Sheath of Light goodness. Delicious.
*It's in my dictionary, why isn't it in yours?