I re-watched this tonight for the first time since seeing it in the theater last fall, and I just noticed all of the business with the 19th hole on the golf course. It struck me as yet another joke von Trier plays on the self-important know-it-all Kiefer Sutherland character, who insists not once but twice during Part 1 that the golf course has 18 holes!
Golf courses do
have 18 holes. If there's a 19th hole appearing in the film, it's a case of von Trier messing with us (for whatever reason), not one of the characters making a foolish mistake. "The 19th Hole" is the bar where golfers go and get plastered after a game, not an actual place.
If Sutherland's character was insisting that his soccer field only had two goalposts, or his tennis court only had one net, we wouldn't dismiss him as a 'self-important know-it-all' simply because von Trier happened to offer us a trippy glimpse of a triangular soccer field, or elongated, double-netted tennis court at some other point.