When Bagger is instructing Junuh about "The Field", (Second Round, first day) he hands him a ball on a red tee. The tee is a plastic one. (Note the shape of the tee having a notch for fingers, rather than a single surface tee). At that era the tees were all wood. Plastic tees were not introduced to the game until almost the year 2000.
During the big 1930 golf match, there are numerous scenes of drinking in a very socially acceptable and legal manner. From 1919 until 1933 the U.S. was under Prohibition. Although there was much laxity in enforcing this law, which led to its being repealed in only 14 years, this was a situation where someone could not have gotten away with violating it.
Bobby Jones tells Junuh he is going to retire from golf after the tournament, which would set this part of the movie in 1930. However, in another scene a movie theatre is showing The Public Enemy with James Cagney, which wasn't released until the following year.
When Bagger is explaining how grass "moves" to Hardy, he points to his right and says the sun rises from there, meaning east, which would mean he is facing north. However, he then sweeps his arm in front of him right to left and states that's the direction of the sun. It's not east to north to west, though-it's east to south to west.
On the first hole of the three man contest, Junuh hits his shot in the sand. The camera shows the ball sitting on top of the sand. When Junuh goes to hit the ball out of the sand, it is very clearly buried in the sand.
On the 18th hole of the final round, Walter Hagen chips a good 3 feet past the hole, and the ball is still moving when we cut away. When he goes to putt out he taps in a putt just inches from the hole.
When Bagger is instructing Junuh about "The Field", (Second Round, first day) he describes Bobby Jones' play move by move and stroke by stroke. He's "In the Field." Bobby Jones then promptly hooks the shot to the left. But the sequence is recorded as though he had sent the ball straight down the middle.
When Junuh is driving his car, he is stopped at an intersection in town by a throng of admirers who completely surround the car; however, in the next shot there are no admirers seen out his back window, and the road behind him is wooded.
The opening scenes tells Junuh's history in flashbacks by zooming in on photos published in newspapers. Newspapers use black ink, which present a challenge for printing shades of gray. A half-tone process was developed in which photos were printed by using tiny black dots that blend in with the white space around them and appear gray to the eye at a distance. In close-up, the photos should have appeared as a conglomeration of dots. Instead, they appear crisp with smooth gradations, suggesting they zoomed in on actual photos instead of a newspaper.
When the score is dead even between all three golfers, you can see the scoreboard showing Bobby Jones and R. Junuh 2 strokes behind Walter Hagen. You can only see this when Junuh finishes talking to Bagger Vance and walks away, because the sign is right behind him.