On the train, the open book on the table in front of Dr. King disappears and reappears in consecutive shots.
When Randy picks up the baseball glove for the first time, a baseball is on the drawer he picks it up from. When they first go back in time, the baseball is gone.
In one scene, Miles and Randy go back in time to see Martin, he is 12 years old. Martin's name was Michael King Kr. He didn't change his name until he was 30. He changed his name to Martin Luther King Jr. on July 27th, 1959.