The magician's full name, Presto DiGiotagione is a pun on "prestidigitation," which means sleight of hand. The rabbit's name, Alec Azam, is a pun on the magic word "alakazam."
The design of the opening credits ("Walt Disney Pictures Presents" and "A Pixar Animation Studios Cartoon") is an homage to the openings of Disney's 1940s and 1950s shorts, which used spotlighted text on a red textured background.
(at around 2 mins) As the magician furiously rushes towards the camera, in the background Statler and Waldorf from The Muppet Show (1976) could be seen seated in one of the balconies.