You don't have to wait until the end of a sequence (such as an investigation sequence or a part of a trial) to save your game. You can save your game any time by simply pressing the START button. This will bring you to the menu where your game can be saved. After saving, you'll be brought back to the start menu.
Those who've played first two Phoenix Wright games in the trilogy should be familiar with a character named Wendy Oldbag. During this game's second trial, "The Stolen Turnabout", there comes a time when you reach a security guard's office. If you examine a sheet of paper in that room, Maya will read aloud "A Guard's 5 Commandments", which is signed by none other than Wendy Oldbag.