Saving progress in Lego Star Wars - The Complete Saga

I'm still figuring out how saving works in TCS but I believe you can only save after you finish an episode. When you are given an option to continue the story or return to the cantina, after you make your selection, a Death Star icon will appear at the top right corner of your screen indicating that the game is saving. Make sure not to close the game while that icon is on the screen.