Finnish runner Juha Väätäinen's name is in then end credits spelled as "Juha Vastinen".
The Olympic Fanfare is heard during television coverage of the 1972 Munich Olympics. However, John Williams didn't compose that piece until the 1984 Los Angeles Olympics.
When the athletes toe the line just prior to the start of the 5000 meter Olympic final you see several of the runners wearing modern running shoes, not the time period track spikes they are later shown to be wearing.
When Bowerman goes to talk to Pre at The Paddock, you hear Donald Sutherland say, "I haven't noticed you working out all that much," but his mouth doesn't move.