Continuity mistake: In the scene where Ferris' mom comes home to check on him to make sure he's really home sick, when she's walking down the hall to enter his room you can see the door knob is a gold/old looking one. When she goes to turn the knob and go into the room, they zoom in on it and it's a crystal door knob.
Continuity mistake: When Mr. Rooney goes to Ferris's house he is wearing a long sleeved shirt and coat jacket. A shot of his arm ringing the doorbell shows a bare arm with dark hair. When they return back to a shot of Mr. Rooney, his sleeve is touching his wrist and he does not have dark hair on the back of his hand.
Continuity mistake: At the end, Jeanie slams the kitchen door in Mr Rooney's face. Watch the pane of glass in the door. In all previous exterior views of the door, the pane is composed of about 4 horizontal pieces of glass. It is apparently a "jalousie" window that opens like a venetian blind, so there are no mouldings between each piece of glass. However, as soon as we see the inside of the door behind Jeanie, visible through the curtain is the silhouette of a "criss-cross" moulding grid, dividing the window into 9 panes of glass.
Visible crew/equipment: When Ferris and gang are driving into the city (Chicago), you hear a song being played and they show an aerial view of Chicago. When they do a flyby of one of the buildings, you can clearly see the helicopter and the cameraman that is doing the filming, in the reflection of the building's windows.
Visible crew/equipment: When Ferris picks up Sloan at school he puts her in the car and walks to the left of the screen. He then enters the Ferrari from the right of the screen. He obviously had to walk around the camera man to do this. You can also see a reflection moving back and forth on the driver's side door while this is unfolding. Presumably the cameraman's.
Continuity mistake: Right at the end, as the Ferrari is flying out into the trees, it lands in the middle of a couple of very large maple trees. In the next shot, when the kids are standing looking down at the car, it is in a clearing, with nothing around it. It is unlikely that the trees were completely pulverized by the car and it was landing directly on top of them so it did not continue to move away after the fact.