The worst part about a pseudonym is that you can't take credit for your work -- which is only a problem if you happen to be incredibly vain. Another downside is that using a pseudonym in contemporary American society appears eccentric, and possibly a little paranoid.
A resoundingly obvious pro is that you are relatively sheltered from the fallout of absurd and offensive remarks. Go anonymity!
People will immediately understand that you are this kind of person however, so remarks by: "twizzle.twinkle.twilight.girl" will pretty much always be ignored.
Another thing that I have considered: given the well-know bias towards subconsciously favoring "pretty people;" if you are of average or above average appearance you should have a picture of yourself. Unless of course, you are prone to making embarrassing, potentially career-destroying statements (see previous paragraph.)
So if you use a pseudonym, do people assume that you are ugly?
Though if you depend on your pseudonym to guarantee absolute anonymity and if you broadcast a lot of information about yourself, then anyone can find out who you are and you are just another idiot on the Internet (who has probably chosen a ridiculous name from science fiction, and then mangled it.)
The good thing about making up a name (especially if your given name is common;) by making it ridiculous enough, you are the only person that comes up on a google search (of course no one bothers to google it, but that's beside the point.)