Account-Wide Achievements and Pets In MoP

In a recently released official blog, Ghostcrawler expressed Blizzard's goal and intent for account-wide achievements. [source]

Pet-Related Achievements
According to Blizzard's current design model, a few achievements will be "account-only". For these achievements, it's unlikely to earn them on a single character, therefore:

...the cumulative work of all your characters on those criteria will count.

Under this guideline players could add to their progression or complete pet achievements such as Legendary Pet Battles (win 5,000 pet battles) on any of their characters.

This will definitely make it more convenient, but don't let that stop you from attempting to earn an achievement all on one toon should you desire to!

Faction-Specific Pets
Ghostcrawler also touches on the topic of faction-specific pets in his latest blog post. Note that there might be exceptions and this entire system is still a work in progress.

You also won’t be able to use a faction-specific pet, mount, or title on the wrong faction.