A Vashj'ir checklist of things that interest me and might interest you too!
Explore Vashj'ir - See the locations listed from the three different mini zones. This comment has a Tom Tom-friendly list of locations and coordinates. Contributes to the meta-achievements Explore Cataclysm and World Explorer.
From Hell's Heart I Stab at Thee - Not sure why this is under exploration, but you kill the Whale Shark.
* The trick is to stay between 6-20 yards of the whale shark; any farther and it will evade, any closer and you get one-shot. There are some good strategies in the comments on Wowhead (mostly involving kiting while maintaining max threat on the kiter) and plenty of videos on youtube.
Sinking into Vashj'ir - the zone quest achievement. The text says 150 quests, but people are getting their completion anywhere between 135 and 150. Contributes to the meta-achievement Loremaster of Cataclysm.
Visions of Vashj'ir Past - do all three of the Battlemaiden quest chains. Quest summaries are here (wowhead comments) and here (wowpedia list).
20,000 Leagues Under the Sea - complete all of the Neptulon related quests up to Defending the Rift. You should definitely get this on the way to completing the zone quest achievement.
[Heroic] Throne of the Tides - completed upon killing Ozumat. The heroic counts towards the metas Cataclysm Dungeon Hero and Defender of a Shattered World, and a guild group will earn credit for the Guild Cataclysm Dungeon Hero.
Old Faithful - During the Lady Naz'jar encounter, kill one of her minions using the geyser ability. This counts for the meta Glory of the Cataclysm Hero.
* There are 2 caster adds and 1 melee add. It's recommended to kill the melee and one caster, then DPS the other caster to 50% health. At that point, wait for a geyser to become available, and deathgrip/silence and kite the mob into the blue circle on the ground. Then, root, stun, or precariously tank it in the circle until the geyser erupts. A priest can Mind Control the add to walk it into the geyser as well. You will get the achievement upon the mob's death.
Prince of Tides - During the Ozumat encounter, kill an Unyielding Behemoth while having Tidal Surge. This counts for the meta Glory of the Cataclysm Hero.
* Only one add spawns throughout the fight, and the buff doesn't come until Phase 2, so you will need the tank to get aggro on the add and kite it while the DPS take care of the other adds. Look out for the conal Blight Spray! Then, once buffed, burn down the add before moving on to Ozumat.
To All the Squirrels Who Cared for Me - Rockchewer Whelk can be found in the Shimmering Expanse, Sea Cucumber can be found in either the Shimmering Expanse or Abyssal Depths.
The Earthen Ring - you can only get to 870 Friendly via quests (beginning at 0 Neutral and earning 3870 rep unbuffed). Provisioner Arok can be found at 49.1, 42.1 in Silver Tide Hollow in Shimmering Expanse.
There are no obtainable non-combat pets from this zone.
Abyssal Seahorse - acquired via the quest The Abyssal Ride, which you get in culmination of this quest chain. Although it can only be summoned in Vashj'ir, it counts towards the mount meta achievements.
* Be sure to dismiss any non-combat pets and disable any auto-summons for said pets, as the bait you put out for the seahorse is considered a pet.
You can catch a high percentage Murglesnout in Vashj'ir. There is also the chance of catching Algaefin Rockfish, Fathom Eel and Deepsea Sagefish in the "Unnamed" Shimmering Expanse. You can also loot Abyssal Clams from mobs in this zone, along with other fish. These will count towards the meta achievement The Oceanographer. There are no pools.
* My recommendation is to quest normally in the zone and loot your mobs. This should satisfy all of these fish. If not, they can all be fished elsewhere (namely Twilight Highlands and Uldum).
You can acquire the following fish/meat for their accompanying recipe to get credit towards The Cataclysmic Gourmet. The number in parentheses is the total amount you will need to cook one of each recipe.
Algaefin Rockfish (1) - Baked Rockfish,
Toughened Flesh (1) - Blackened Surprise
Deepsea Sagefish (2) - Delicious Sagefish Tail, Severed Sagefish Head
Blood Shrimp (from Abyssal Clams) (2) - Hearty Seafood Soup, Whitecrest Gumbo
Fathom Eel (5) - Skewered Eel, (one component of) Seafood Magnifique
Monstrous Claw (1) - Seasoned Crab
Giant Turtle Tongue (1) - Tender Baked Turtle