Protection/Fury is kind of a no-brainer at this point. Both specs work pretty well, and almost all warriors have a DPS set and a tanking set anyway. The only real issue is in the minutia of gearing: does the warrior have a suitable pair of 2h weapons? Gear is the real limiting factor in any and all uses of dual spec for warriors, with glyphs also being an issue, but since glyphs will change with the talents (after the initial cost) you'll at least only have to assemble your 'off spec' glyphs the one time, while you'll have to update your gear as you progress. This won't be terribly onerous, because you were probably going to assemble an off-set for tanking or DPS anyway.
Sadly, Protection/Arms doesn't seem as likely in PvE. Arms is underperforming, but I said that I would ignore that for the purposes of this analysis. Assuming that PvE arms catches up to fury in damage (honestly, I don't think it can without heavy work but that's for another day) arms offers some solid debuffs but none of them require a warrior anymore, other classes can provide them, and fury just has more visual oomph. Still, a PvE Prot/PvP Arms or even PvP Prot/PvP Arms set up makes sense.
Right now, with the state of warrior PvP being what it is (pretty bad) and with dual speccing still requiring an inscription-made item and several players to accomplish, I expect we'll see either prot/fury where the prot spec is used as a PvP spec or prot/arms with both specs used as PvP specs depending on where the milieu is. I've found arms can still be wildly successful in BG's and Wintergrasp (and by the way, I'm not happy that you people have somehow worked black magic to get me to participate in Wintergrasp) but when I arena I tend to go prot or a specific fury build with Heroic Fury and Furious Attacks in it. These are not talents I use in PvE, which does lead me inexorably to the idea that some players will actually spec PvE and PvP within the same spec. If I were more serious about arenas, I would probably spec fury (PvE) and fury (PvP) myself.
It may seem ridiculous to consider having two nearly identical specs, but we all know that a few talent changes can make a spec perform entirely differently. Just cobbling together two different prot specs, we can see how this would perform differently than this. Looking over both you can still see some glaring omissions (Imp Bloodrage, Imp Disciplines) that you might really want in some situations but not need in another. To use another example, this is a fury build aimed at DPS in PvE (it's the one I use, as my gear supplies all the expertise I need) whereas with the change of three talent points it becomes much more focused on mobility and debuffing opposing players with Furious Attacks. You could change it more by working Enrage back into the talent selection but with the current state of burst in PvP, if you're getting hit a lot you'll probably be dead before you can use it. YMMV, of course.
I wouldn't be surprised at all to see warriors with a grinding/heroic tanking talent spec and a raid boss tanking spec, or a PvE arms/PvP arms tree. It cuts down on the gear selection you'll need to make, for one thing. It won't last forever in the case of PvP/PvE specs... eventually Blizzard will find a way to make resilience gear work again, and then we'll see you with a full PvP set unless you PvP prot, in which case I expect tanking gear will still suffice with its gobs of stamina and defense. The main weakness of a warrior in PvP is magic, and prot's about as well suited to deal with magic damage as any warrior tree could possibly be with spell reflection. (Yes, any warrior spec can use SR, but prot usually has the shield right out and doesn't have to run a macro.) Warriors tend to go the extra mile in their talent selections, ruthlessly pruning away until they find the right bonsai for the situation, and the ability to choose between specs means that you'll definitey expect to see at least a few who have a job they really like to come up with ways to use this situation to their benefit. Let's face it: we all know some warriors who just aren't very good tanks, or who underperform as DPS, but who excel at their chosen task. Just because dual specs gives you the ability to more easily put a petticoat on a hippopotamus doesn't mean you have to.
In fact, this is something I worry about. We all know that in raiding we generally use more tanks on trash than on bosses and some boss fights require multiple tanks, while others require one or two at most. With dual specs, the pressure for warriors will be to have a tanking spec and a DPS spec, just because that's basically what a warrior can do in a raid, tank or DPS. Raid leaders tend to try and squeeze maximum benefit out of each player for the raid, it's their job. Raiding warriors will have to expect a certain amount of pressure to select talent specs that can most easily be used to benefit the raid. You can't really fault them for this, and to a degree the presence of so many potential tanks in endgame will insulate warriors from this pressure to some extent. Since you can expect paladins and druids to be pressured to spec healing as their offspec to some degree (unless they're already a healer) it probably isn't a major concern, but it does exist and should be mentioned. If you intend to use dual specs to have your 'raiding' spec and your 'me time' spec, be sure your raid doesn't expect differently from you.
In the end, at least for warriors, dual specs doesn't have a lot of down sides. At worst you'll be expected to have a tanking spec and a DPS spec for raiding, which for a lot of us is more or less what we want dual specs for, so it's like being sternly told that you're expected to eat all that ice cream. For those of us who don't raid, it still opens up a lot of possibilities in terms of freedom to run BG's and arenas all day and then pop out and tank a heroic for a friend, or even to allow a dedicated tank who could care less about fury or arms to have a spec for heroics and normal five mans that he outgears and another for tanking harder-hitting bosses (especially as Ulduar opens up), or a Titan's Grip junkie like myself can easily shift three talent points around for the ultimate in min-maxing.
And finally, the ultimate pro of the entire dual spec system, the feature they could have rolled out all by itself and I think every warrior (indeed, anyone who respecs a lot) would have said yay.
Ghostcrawler: With the dual spec feature, we are going to allow players who respec to configure all their talents before they get saved. They will be able to allocate the points, then choose if they want to use that as their spec, rather than needing to carefully diagram out their talents ahead of time. This will allow players a little more freedom when deciding on the talents they want to pick and avoid costly mistakes.
I know there are addons that do this for you. Frankly, any time the game automates something so I don't have to have an addon to do it, I squeal in glee like rubber sheets with the aforementioned hippo rolling around on them. And yes, I'm going to end this column with the image of a hippo in a petticoat rolling around on rubber sheets. No need to thank me.
Next week, or maybe this weekend if there's enough demand, hit and expertise for DPS warriors. Unless Blizzard announces that Titan's Grip is going to be a baseline talent or something. I'd probably just pass out if that happened.