Revealing mistake: After Jim's horse is shot from under him while running down the really steep hill, and Jim later regains consciousness, before he turns and finds his horse dead, if you watch closely you can see the horse still breathing.
Continuity mistake: In the scene before the race, the butler is leaning against the wall smoking. When he gets off the wall, there is a large grey smudge on his black suit, but the next time we see the back of his suit there is no mark. (00:13:00)
Answer: Denny.