Instructors usually teach as long a sequence as they can in a lesson, guaranteeing that I won't remember any of it.

If the sequence is too complicated than you are taking a class that's above your level.

If you have done a lot of Salsa lessons than you might feel that you should be able to go to the intermediate level classes. If you however can't follow those than you should continue with the beginner classes.

But in dancing salsa, the man needs to keep in his head a list of about 100 different moves or short sequences, and every 4 seconds, he needs to review what he's just done and choose a new one that fits the previous sequence but isn't mere duplication of it.

Duplication isn't that bad. It doesn't prevent you from having a fun dance on the dance floor. You don't need 100 different moves either (if you define 1 moves as what you dance to 8 beats). You don't need to review anything. You just need to make a new move from the hand position in which the last move ended.