(at around 1h 10 mins) When Thompson addresses the college students in the auditorium, he lights a joint with a Bic lighter. The scene took place in 1972, and the Bic disposable lighter wasn't invented until 1973.
In the bathroom scene when Murray is washing his shoes out in the sink, then hits them repeatedly against the urinal to get the excess water out, he is wearing glasses but his reflection in the mirror behind the urinals isn't.
During the courtroom scene, 21 minutes and 5 seconds into the film, Thompson sets down his glass which is almost full. A second later, a close-up on the glass shows it sitting on the floor, empty. All further scenes in the courtroom show the glass once again almost full.
When Dr. Thompson goes to college to "lecture" the students, he lights up a joint, takes a few hits off of it and then moments later lights up yet another joint before finishing the first one (or passing the first one along to anyone else) basically showing that he lit the same joint twice.