Lydia (Debbie Allen ) was a student in Fame (1980), not a teacher as is commonly thought. She was an older student who was just supposed to be helping with the auditions. There were a couple of deleted scenes which show her facing off against Coco, who was supposed to be a peer and a rival of hers. When the producers asked Debbie Allen to come back to do this show, it was two years later, and she was obviously no longer a high school student at that point. Because of that, and because the editing of the original movie wound up making her look like a teacher anyway, they changed Lydia from a student to a dance teacher for this show.
Madonna tried out for this show. She didn't make it, but they kept her audition tape, it's available on YouTube.
Erica Gimpel (Coco) is missing from the last several episodes of the first season because she was completing her own high school education.
Janet Jackson, who appeared on this show for one season as Cleo, this being the third television show, on which she appeared, after Diff'rent Strokes (1978) and Good Times (1974), claimed that she and the other young cast members were mistreated by the producers, and consequently quit before the season was over.
Although mostly shot at MGM studios in Culver City, California, the cast and crew made at least one trip to New York City each season to film exterior scenes in advance of the rest of the episode's shot in Los Angeles.