Question: What happened to Flounder's girl Sissy? Flounder never mentions her after he brings her to the toga party.
Question: Why didn't the mayor try and have the Deltas arrested for both the mayhem they caused at the parade and that one of them may have had fun with his underaged daughter? Obviously the audience knows the member didn't but the mayor doesn't.
Answer: There's no indication that the Deltas didn't face legal ramifications from their actions at the parade, nor that Pinto didn't get in trouble (when we last see him, he's literally being chased by the mayor). The film ends at that point and, although the film provides title cards telling us what happened to the characters far in the future, we don't see the immediate aftermath.
Question: Near the end, when Dean Wormer and Mayor DePasto are in the grandstand, officially launching the parade, there is an elderly gentleman in the background (also in the grandstand, about 2 levels up, on the left side of the screen) who is making odd, excited gestures and comical facial expressions. His appearance and odd mannerisms are so striking that he draws my attention away from the dean and the mayor every time that I've seen this film, and that's a lot of times. Surely, director John Landis must have been aware of the gentleman and his antics in the background through multiple takes, so it would seem Landis intended the peculiar distraction. Who was that gentleman, and was there any significance to his appearing in the scene?
Answer: Sometimes these things get left in because it's simply the best take. (The child covering his ears before the gunshot in "North by Northwest," for example.) It could also be that John Landis cast the extra because he wanted someone with goofy expressions in the crowd. He simply could have told the extras "Ok, be excited that you're at a parade," and that's how this extra did it.
Answer: Nothing "happens" to her, she just isn't in the movie anymore. She's only in a single sequence and is completely inconsequential to the plot, so there's no need for to the film to address her or her movements after the party. Flounder has no reason to mention her.