Cloud Cuckoolander: Has shades of this. In the first season, for example, he seems ignorant of the most basic hygienic considerations, but in the next breath demonstrates considerable knowledge of acting and filming techniques and famous movie directors.
Childhood Friend Romance: Plans to invoke this trope on Melissa. In one episode he explains his incredibly detailed marriage proposal he's planned.
The Pigpen: Though this was largely downplayed after season 1.
Spell My Name with an S: A running gag on the show is that his family name is spelled differently everytime it's shown on-screen. "Penopolis" was the first spelling used (excluding an earlier episode where it was spelled as "Panopolis" in closed captions), followed by "Popodopolis" and "Penopopolis".
The Other Darrin: Played by Paula Poundstone in the first 5 episodes (the ones that aired on UPN). Then, when the show was Un-Cancelled and put on Cartoon Network, she was played by Janine Ditullio for the remainder of the series.
Book Dumb: He's an incredibly talented guitarist and wrote a compelling movie script in "Director's Cut", but is apparently bad at his high-school studies. It doesn't help that he has no real interest in school.