Revealing mistake: When one of the men picks up Garfield from his cage to display to potential buyers at the pound, you can see the man's right hand "entangled" with the computer-generated Garfield.
Revealing mistake: When Garfield and the mouse are going down the street underneath cardboard boxes, you can see the wheels of remote-controlled "cars" that were used to create the illusion. It is especially obvious in some of the scenes of the mouse, under the Chinese-Food box.
Revealing mistake: When Garfield is in the air vent, he falls out into a box, which topples over. The Garfield that falls into the box is motionless, in a crouched position, and obviously a stuffed toy.
Revealing mistake: When Garfield and Jon first bring Odie home, you see Garfield talking to one of the neighborhood cats outside while Jon has gone inside with Odie. You can see a colored square on the sidewalk where the neighborhood cat sits. Throughout different shots in the scene you see the square disappear and reappear.
Answer: The song is called "Holla", by the Baha Men (of "Who let the dogs out" fame).