Goof (revealing mistake): Michael obviously wasn't playing the guitar.
Goof (crew or equipment visible): When Michael is walking into the kitchen to show Junior and Claire the payphone, a crew member can be seen through the window off to the left side of the screen, standing in the kitchen.
Goof (revealing mistake): There is clearly no image visible on the Television when Michael is playing the Gamecube.
Goof (errors made by characters, possibly deliberate errors by the filmmakers): Junior says that he has $600 and Michael says he'll match it. After Junior says "That makes $1000", Michael says "Why don't I add $300 and make it into $1200?"
Goof (errors made by characters, possibly deliberate errors by the filmmakers): Junior states that Hamburger University is one of only two schools that would even consider accepting him. Hamburger University is only for management and franchisees of McDonald's. Unless he were to become a manager or franchisee, Hamburger University wouldn't actually consider accepting him in real life.