The most notorious bug is the "cancel friendship" bug. If you want to cancel a friendship, you go to the page of the friend you want to cancel and click the "Cancel Friendship" link. Simple, right?
Except that it when I have done this either accidentally (yes, it did happen accidentally a couple of times) or purposefully, it did NOT cancel that person, but someone else (seemingly random). I know for a fact that I am not the only one who has experienced this.
Another strange bug is: Player "x" sent me a friendship request; I accept. Player "x" is listed in my friends list, but I am not listed in theirs. In an attempt to correct this, I tried to "cancel friendship" (Player "x" requested I do so - the thought was for me to cancel then re-request to see if that would work), only to find that someone else disappeared from my list (that most notorious bug rears it's ugly head once more).
I suppose one could just keep hitting the "cancel" link until either the actual person you want to cancel is removed or there is no one left your "friends" list. Talk about using a cannon to kill a fly...