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.
Continuity mistake: When Cameron is on the phone with Mr. Rooney pretending to be George Peterson, Ferris calls the school. Grace picks up the phone in the outer office and tells Ferris to hold. You clearly see the third button (line three) is the one he called on. Grace says that Ferris is on line two. When Mr. Rooney puts Cameron on hold and listens to Ferris, after Ferris hangs up, the camera cuts to the phone buttons on Mr. Rooney's phone showing that Ferris was just on the second button (line two).
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.