Have no fear! A spam filter or solution is in the works. The first day the FB app was introduced I made it a point of spamming every developer sim I could find with a message.
"Spam-o-gram".
I'm pretty sure they are aware of the problem
You don't actually receive anything other than an alert that someone has posted a message on your Facebook avatar's wall. To actually read the message you have to login to Facebook.
So far the only thing that prevents you from getting these in-game alerts when you login is to put that person on ignore. I hope they come up with a better solution.
Once we have the abilitity to control our own friendships, I would imagine we will have a setting to allow these types of messages only from friends.