When Sarah asks Francis his name, he pronounces his surname (Ouimet) wee-MAY, yet she pronounces it wee-MET. She wouldn't pronounce it as such from his pronunciation, she would have had to have seen it written down to pronounce it that way.
Harry Vardon is credited with inventing the "Vardon" grip, which involves the fingers of the hands overlapping. During the golf scenes both Vardon and Ouimet were using the "interlocking" golf grip, which is contradictory to the "Vardon" grip. One would think that Vardon would use the Vardon grip.
Going into the fourth round of the 1913 U.S. Open, it was stated that Ouimet was trailing Vardon and Ray by one stroke. Yet, the final leader-board showed all three of them shooting 79 with a total of 304 strokes for the tournament. This would have meant that they were all tied entering the fourth round.
Near the end of the round, Ouimet and Vardon are shown hitting several shots at a very quick pace. At one point Ouimet is shown swinging left-handed. When he played every other shot in his round from the right-handed position.
The seventeenth hole of The Country Club is shown as a dogleg right, and Harry hits his ball into an unseen trap on the right side of the corner of the dogleg. In reality, the seventeenth hole at The Country Club at the time of the 1913 US Open was a dogleg left, and Vardon hit his ball into a trap on the left side of the fairway.
The opening shot of the movie begins with a scene set in Jersey overlaid with the caption "Isle of Jersey, England". The island of Jersey is one of the Channel Islands and is the main island of the Bailiwick of Jersey. It is closer to France than to England and is neither geographically nor administratively part of England or even the United Kingdom, but a British Crown Dependency with its own administration and the British Queen as the head of state in her capacity as the Duke of Normandy.
Francis is shown looking at a yardage book, or a series of hand drawn diagrams of every hole at The Country Club. In reality, yardage books did not come into use until the 1960s, first by Deane Beman and later popularized by Jack Nicklaus. Harry Vardon is shown laying Francis a "stymie" during the playoff. A stymie occurred when a player's ball blocked the path of his opponent's ball on the green (the balls not being within six inches of each other). This only applied to singles match play. The playoff for the 1913 US Open was medal (stroke) play and the stymie rule would not have been in effect. This rule was eliminated in 1952 by the USGA.
On the 18th green, Vardon misses his first putt, then holes out. While this is common in present day golf etiquette, the practice in 1913 was strict, and Vardon would have received a penalty. The player who is farthest from the hole (away) plays first. While in present day, it is common to hole out, the rule is still that the player who is away plays first.
In the playoff round, they pan across the 3-player scoreboard very quickly and at the end we see Quimet and Vardon tied at Even. Below their score is Ted Ray at +6. If you go back frame by frame and look at the scores on each hole, we see that Ray is really only at +3 up until this point in the match.