Joseph Gordon-Levitt only appeared in a little over half of the show's episodes in the final season (including the series finale) so he could concentrate on his Columbia University studies. The former child star told Details how he was "scared and depressed" for a time, fearing that he wouldn't be able to find acting work ever again.
The story of how French Stewart came up with Harry's squinting look is somewhat of an accident. He had done his first audition for the show. Feeling the audition went well, he went home and decides to take a bath while smoking from his bong. His agent then calls him and tells him that casting wants to see him again right now. He asked his agent to stall them for an hour so he could get his head straight. When he returned, he had a more squinted look in his eyes. Casting noticed his squinting, but they liked the difference in his performance.
Jane Curtin originally signed on for just seven episodes in the first season. When she finished taping her fifth appearance, she decided she wanted to stay, and remained on the show as a series regular for the rest of the show.
Eight days after the airing of the season three finale, Phil Hartman was tragically murdered. When the episode re-aired a week before the following season's premiere, Hartman's scenes were re-shot with a different actor as a different character, so the resolution to the cliffhanger involving Hartman's character wouldn't seem awkwardly re-cast or possibly considered disrespectful.