Factual error: When the second round of the tournament is starting and Bagger Vance is telling Rannulph Junuh about 'the field', just after Bobby Jones has taken his tee-shot, Bagger hands Junuh a ball and tee. The tee is a red plastic 'castle' style tee. Apart from being illegal in tournament play, I'm pretty sure they weren't around in the 1920's.
Factual error: On the final hole of play, Damon should have placed his ball back to its original position and taken a one stroke penalty. He did not replace the ball to its original penalty, so he would have been deemed to playing the ball from the wrong position, which is another penalty stroke.
Factual error: While on the final hole, last round, the camera pans in on one of the men "inside the ropes" with the three golfers. He is wearing glasses, and they contain a greenish reflection of the late afternoon sun. This colored reflection is due to a modern anti-reflective coating put on lenses today to prevent annoying reflective glare. These coatings weren't available until the 1980's and in wide use until the 90's.