Just after Millman is rejected by the Coach in the Olympic letter scene, Millman and Socrates are talking in the Service Station. Behind Millman, Socratese is reflected in the glass of the window. His lips are moving and he shakes his hand but the audio has no dialog from Socrates at that exact moment. In the final scenes, when we see the gym and the Olympic try outs, we hear cheers and applause, but only the people sitting in the first three or four rows of the audience directly in front of the viewer are clapping.
While Dan and Socrates have a conversation in the garage, Socrates is organizing and placing small boxes into a cabinet door. The very last shot of the cabinet shows the boxes in a different arrangement than they were during their discourse.
During the motorcycle accident in several of the slow-motion shots you can clearly see that Dan has the green light and the man driving the car has a red light but we are led to believe that Dan caused the accident. (It is stated and repeated by Dan's teammate in the following scene that Dan ran the red light.)
During a conversation Dan's teammates are having, they are in awe that Dan is attempting to do 3 consecutive flips on the rings because no one has ever done that before. Well in a competition, it's illegal to repeat a skill more than once in a routine.