In New Game +, tap Up, Up, Up, Up+A at any point to fly.

Complete the game and select New Game + from the main menu. When you reach the point in the story where you recieved the Fez on the first play through you will get a pair of sunglasses instead. These allow you to view the world in first person by pressing in the left analog stick.

Collect all 64 Cubes and then go back through the Star Gate in the 32 Cube room for a different ending. After the credits, select New Game + one again from the main menu. When you reach the point in the story where you received the Fez and the Sunglasses the first two times you now get a pair of red/blue 3D glasses instead. These automatically enable Stereoscopic Mode, which can then be disabled in the Settings menu should you not want to use it.