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.
Before the NCAA championship the movie shows Pre injuring his foot in a hotel room with "Iowa's Finest" (Amy Jo Johnson). Pre actually hurt his foot jumping into the hotel's pool from the lifeguard post.
In the restoration meet, Pre was shown before the race as scared and unsure of himself against tough competition. In actuality, for this race, Pre was upset at the lack of competition in this race.
The custom shoes were known as Blue Ribbon Sport's (BRS) and eventually became Nike not Adidas.
The Olympic Fanfare is heard during television coverage of the 1972 Munich Olympics. However, John Williams didn't compose that piece until the 1996 Atlanta Olympics.
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.