When Bart and Lisa are in the living room talking to Homer and Marge, there is a drawer above a shelf with a book in it. The shot then cuts to Homer and Marge. When it cuts back to Bart and Lisa, the book is gone.
When Marge and Homer are talking at the entrance to the campus, the professor arrives with his jacket on. In the next shot, it's gone.
When Homer throws his cigar into the oxygen bar, it explodes. Oxygen would not cause an explosion, rather only a quicker burning of the lit cigar.
When Homer's group is shown in the recording studio, the knob on the mixing board's fader is horizontal instead of vertical.