When Professor Ned Brainard uses the weather machine to cause a rain cloud inside Shelby's car we see the car get flooded and Shelby floating around, yet without Shelby's foot anywhere near the gas pedal the car still keeps driving.
As the football team runs onto the field for the climactic game, a banner that reads "Burbank High School" can be seen in the background. This is not one of the fictional schools involved in the match.
Professor Brainard was not filmed in the changing room in "The Absent-Minded Professor", and the basketball game was not filmed either. However this appears in the Flubber advert.