Continuity mistake: When Rooney gets out of his car and walks up to Ferris' front door his jacket is unbuttoned, when he gets to the door it is buttoned.
Revealing mistake: In the taxi scene Ferris' dad is reading a newspaper. On the front page is an article with the headline "Community rallies around sick youth." As the camera zooms in it's a fake headline to a real news article. The news article begins, "A Chicago policeman killed himself today after he... a Park Ridge office and... workers with a... revolver as he searched for his estranged wife who was hidden beneath a desk by a fellow worker".
Continuity mistake: When they are at the pool. Sloan asks Cameron if he watched her change into her bathing suit, but based on the scenes in the pool, she was wearing undergarments and most likely just took off the outer layers.
Plot hole: When Jeannie encounters Mr. Rooney at her house, she attacks him and calls the police. Later, the police pick her up for filing a false report. Why? Surely they would've seen signs of an intruder such as a dropped wallet on the floor and footprints in the mud right next to the house.
Suggested correction: Without knowledge of what happened when the police visited, it's impossible to call this a plot hole. It might be that the police knocked on the door, Jeannie answered and explained that by the time they got there the intruder had gone. She could have got angry at them like she did on the phone. Maybe they arrested her there and then, without entering the house or searching the grounds (for someone they'd just be told was no longer there). Who knows? Unlikely sure, but not impossible.
Continuity mistake: Ferris steps out of bed and raises his arms in an 11 O'clock position to open the blinds. From the angle behind the arms are raised in a 3 O'clock position.
Continuity mistake: When the movie starts, Ferris's in bed, his fringe all over his forehead. A frame later it's brushed sideways.
Continuity mistake: After Ferris picks up Sloan from school in the Ferrari, he is seen speeding off towards the end of the parking lot (there's an exit and then a few more stalls before the end of the lot). He gets into 2nd gear before it cuts back to a shot of Mr. Rooney. As we see Rooney's face, we hear the Ferrari running through 2nd gear and into 3rd. This is impossible as they would've had to slow down to make the exit or they would've run off the end of the lot.