When Socrates walks outside the service station door and sits down, the trash can is on the right. When the camera returns, the trash can is on the left.
In the conversation with his coach, Dan's first tear disappears between shots.
In the crash sequence, Dan lands in a shower of safety glass chunks after going over the car. When the scene moves to another shot, all of the car's windows remain intact.
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.
The gymnastics room is painted sky blue and gold which are UCLA colors. Cal colors are (very) dark blue and gold.
In the final competition, there's no vault or floor as there would usually be in a competitive gym.
Dan's stunt double is easily identifiable by the different arm muscles and shoulder broadness.
The second time Dan asks "What time is it?" his lips never move.
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.