As Emperor Devon said, class only affects two things, one in a conversation with Carth and one with Bastila. Both times they are asking about your background, and only pertain to your first class, not your Jedi class. For Carth, there's a difference between what his says in response to your answer if your class is scoundrel instead of soldier or scout. Basically, he just is a bit suspicious about your background as a "smuggler"- but it doesn't actually effect gameplay. For Bastila the response is the same no matter what class you are.
As for alignment- well, certainly your actions affect dialogue. For example, if you kill Juhani instead of convincing her to return to the Jedi, the Council chastises you instead of congratulating you when you return. Basically any quest has different turns in dialogue if you do the Dark Side resolution, Light Side resolution, or neutral resolution.
As for if your general alignment affects anything- as far as I know, only conversations with some party members are affected. The biggest affect is that it's basically impossible to do the romance with Carth if you are a dark side female.