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.
During the Case 5 ending credits on the touch screen, fingerprint powder will be applied and blown away to reveal the credits. A dialogue scene with a character will appear. Tap the touch screen as though applying fingerprint powder to it and blow it off. A hidden drawing of that character will appear on the top screen.