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.
Continuity mistake: In the parade scene where Cameron and Sloane rush out attempting to get Ferris of the float, they are approached by a police officer wearing a black jacket. Seconds later there is an aerial shot of the parade, and C and S are being led back to the kerb by a police officer who has no black jacket.
Continuity mistake: When the flower deliveryman goes to leave the Bueller house, he toots the horn before speeding off after Rooney flips him the bird. It then cuts to a wide shot of the front of the house and the van is gone. We never hear the van's tires clearing the bump between the driveway and the road, and the van would've had to be going excessively fast to have cleared the driveway in the time between hearing it set off and the wide shot.