When Joe opens a homemade card, there are two flowers inside. When shown again the flowers are missing.
The newsreel in the movie says Jesse Owens is from the University of Ohio. While there is an Ohio University in Athens, Ohio, he was actually a student at The Ohio State University --- so named in 1878, well before 1936.
The railway send-off scene to Poughkeepsie, NY, shows an English Great Northern Railway train and not an American Great Northern Railway train.
When the team is to travel from one part of the US to another via train, they board a British train with doors at each compartment, pulled by a British steam locomotive.
In the Poughkeepsie scene, one spectator boat had its name on the back on a large white banner using the Arial font. The Arial font was created in 1982 by two Microsoft employees wanting an alternative to Helvetica, 46 years after the year (1936) in which this movie was set.
Joe's father in America is shown following the race on a radio. The radio is a British-made Bush radio rather than an American model.
The railroad cars and trains in "Seattle," "Poughkeepsie," and along the "Hudson" River are all British.
In the scene where coach announces he's going with the JV team, the band is using white fiberglass sousaphones. They weren't invented until the 1960's.
The popular Christmas song one of the team members plays on the piano in the theatre clean up scene at about 33:48, "Here Comes Santa Claus (Right Down Santa Claus Lane)" written by Gene Autry, Oakley Haldeman, and Harriet Melka was not yet written. It was published in November 1947.
The water used for both Lake Washington and Poughkeepsie is not filmed there. Lake Washington is HUGE and has no narrow waterways as in the movie. It appears they filmed from one bank for Lake Washington scenes and the other scenes from Poughkeepsie.