I've heard of this not specifically with vet apps, but for things like job applications, and other professional schools (so yeah vet school in that case!).
All the things I've seen were on the news, and I think the general message is 'Don't be an idiot'. If your facebook profile is private or invisible, then people outside your friends can't see you or anything on you profile.
My e-mail address for vet school (i.e. my "professional" e-mail address) isn't the same as my facebook log on, and my name on facebook is my first and middle name. I didn't specifically do this for privacy and so that employers can't find me, it just worked out that way, but essentially serves the same purpose.
I don't think its necessary to go all paranoia and delete your entire facebook profile page, but just be smart about it, and don't tag photos of yourself where you're piss-drunk, half naked and posing with a shot gun and a bloody deer or something.
Wanted to add:
in addition to what Libster06 said, I'm not one to update every minute from my iphone: "walking the dog!", "saw the cutest squirrel on my walk!" "soo hot out! really want to go for a swim!" "Swimminggg!! <3!" ... etc, (not to mention my lack of iphone-ness), but Facebook is also excellent for keeping in touch with people you meet while traveling, and sharing pictures of your travels with your friends/family to let them know you're still alive, and also to make them extremely jealous. Facebook is quicker and easier to message a friend in another country then e-mailing, and its more fun because you can see their pictures, live chat, etc. Its also an easier way to remember who's who rather then trying to remember if
[email protected] is that hot guy you met on the ferry to Montezuma, or that really cool mom of 3 you met while you were lost in the middle of Auckland.