Others have discussed this topic at length already, but I wanted to throw my hat into the ring as well.
Let me start off by saying that I rather enjoyed the zone as a whole, but I do have to add the caveat that this was my first playthrough and that I did the entire zone solo. I think the latter bit is particularly important because from questing with my boyfriend I've got the impression that "the new WoW" is actually not particularly group friendly. As Zelmaru pointed out in a comment elsewhere, the frequent phasing means that you can only level with someone else if you are in "lock-step", since you can neither skip ahead nor go back to help your friend kill things that have already been phased out for you.
Contrary to what some people hopefully proclaimed after the Shattering, collection quests don't all have a hundred-percent drop rate either. My boyfriend and I got started on Uldum today and I lost count of how many times we had to circle the same spot of desert, killing pygmies for their stupid rare drops, just to complete a simple quest for both of us.
Some quests are also more likely to just not work properly or bug out if you try to do them in a group. For example there was this quest in Mount Hyjal where you were supposed to trap and interrogate a harpy, and I was very confused that I didn't get any dialogue options when I tried to talk to her... and then she suddenly dropped dead and I got a quest completion message. Turns out that only my boyfriend had been allowed to question to her. Lame. Or in early Uldum we completed a quest at the same time and while my boyfriend got to watch a cut scene afterwards, the quest giver just phased out quietly on my screen. I could go on and on...
Anyway, Vashj'ir. The sad truth is, questing alone actually made it easier for me to enjoy the story since things went much more smoothly that way. I only had to worry about gathering crab meat or whatever for myself, nothing got borked up for me just because my boyfriend clicked on it two seconds earlier, and I found it easier to suspend my disbelief and believe the NPCs' constant praise of my unique talents and heroic deeds.
While the zone is still extremely linear, I do admit that it felt a bit less constraining than the worgen starter area, because at least I was never completely locked into a four by four market square or anything of the like. I could still swim around and explore the entire zone if I wanted to, even if many areas seemed oddly empty if you were visiting them in the "wrong" phase. I only ran into an obstacle on the rails once, when I finished everything at a hub but couldn't pick up any follow-up quests. I then went back to the area where I had completed the last couple of quests and found a completely unrelated quest giver in a corner somewhere, whose quest then unlocked the rest of the zone for me. In the end it turned out that he wasn't completely unrelated as he became a recurring character, but it still felt clumsy to me that he was placed somewhere where he could easily be overlooked if he was that important to the plot.
Many of the quest achievements also felt kind of pointless to me. For example, you can't get 20,000 Leagues Under the Sea without completing Visions of Vashj'ir Past and Sinking into Vashj'ir as well, so why have separate achievements for those anyway? Fancy names aside, they are basically all equivalents of "complete x quests in Vashj'ir". Felt to me as if Blizzard was worried that if players weren't getting an achievement pop-up at least every so often during their way through the zone, they might get bored...
There were a couple of quests independent of the main storyline by the way, but they were thoroughly unimportant. For example you'd kill a wandering Alliance NPC, get a quest pop-up saying something along the lines of "Alliance, here? You better kill them!" and then that was it. Didn't really make me feel like I had discovered a great little Easter Egg or anything.
Also, the seclusion of the storyline made suspension of disbelief harder for me than usual. You're supposedly helping out these ship-wrecked survivors with no contact to the outside world... but for convenience's sake, you can stop at any time and then hop through a portal in Orgrimmar that will take you right back to where you left off. MMOs have always requried a lot of suspension of disbelief, but if all NPCs are stuck in the same place and time forever, at least that's consistent. However, having my questing move the story onward, until the point where I decide to hearth and it all magically freezes in time, is once again a whole new kind of awkward. I like the idea that the world goes on without me, that's part of the appeal of an MMO.
Many of the quests themselves also weren't actually that inspiring. I'm tempted to keep a record of my next playthrough and count just how many quests are basically a variation of "kill some naga", because I got the impression that it's a very large percentage. Good thing that I like naga. They are probably my favourite NPC race and if they ever became playable I'd happily roll a dozen.
I particularly liked the battlemaiden quests for that reason, but also because my character "playing" yet another character felt like diving into an additional layer of roleplaying to me, and even as someone who hasn't actually roleplayed much in WoW in a long time, I really got into the spirit of being the battlemaiden, appreciating her fierce loyalty to her cause and the way one of the male naga quipped with her about who got to do more killing. Why wasn't she around in the end? With her abilities she would have made for a fierce raid boss...
Since I'm talking about likes now, I should probably also mention that I really liked the look of the zone. For some people that might be a minor thing, but for me it's very important. If I don't enjoy the way a zone looks, I won't ever enjoy questing there either, regardless of the actual quest content. Deepholm for example was a big turn-off for me simply due to being nothing but black rocks overlaid with more black rocks. The underwater movement in Vashj'ir didn't pose too much of a problem either, though it probably helped that I was going through the zone on my druid, whose instant-cast aquatic form was often more efficient than even the seahorse.
The ending to the major quest line struck me as very weak, unfortunately, because it was basically one endless cut scene - except that for the first ten minutes or so it's not even apparent that it's a cut scene. I can pretty much agree with Adam's spoileriffic account of it here because my own experience was eerily similar, except that as Horde I was dealing with goblins instead of gnomes... and I got stuck behind one of the submarine's pipes while bouncing around in boredom and was about to hearth out in disgust when a cut scene mercifully ejected me. Who designed these bloody ships anyway? I managed to get stuck on the Alliance airship in Deepholm the other day as well.
Anyway, tl;dr version:
Things that I liked about Vashj'ir:
- Smooth single-player story progression
- Pretty to look at in a Little Mermaid kind of way
- Naga everywhere, and you even get to play one for a little bit, yay!
Things that I didn't like so much:
- Too much linearity and all its associated problems (awkward time flow, redundant achievements, getting stuck)
- The final quest basically being one huge, boring cut scene.