Archive Panic: Sure, they might have only five studio albums, one live album, and an EP (in addition to a few B-sides here and there), but since bootlegging is encouraged at their shows, almost every concert they've ever played can be easily downloaded. The result? Several dozen gigabytes of MP3 files to hear all of their live material. Necessary for completionists because they frequently mutate improvised sections into new songs, and even those that aren't reused still kick ass.
Broken Base: not very prevalent actually but there are certain fans who will argue over the better drummer was Pridgen or Theodore, it's almost certain that Elitch will be a topic of argument.
Elitch was apparently only a temporary drummer, and he's been replaced by Deantoni Parks, someone the fans can all pretty much agree is a good fit (because really).
Face of the Band: Omar and Cedric, but justified that it is explicitly stated in the liner notes for Amputechture that they are The Mars Volta and that the rest of the band are part of The Mars Volta Group.
Recently Omar has stated that he wants to make The Mars Volta more of a democracy.
Ho Yay: Honestly Omar and Cedric are very guilty of this.
It's gotten to the point where Omar acknowledged it in an interview