Revealing mistake: Throughout the extended scene where Ralph was training with Father Hibbert in pouring-down rain, both characters' faces were completely dry when they should have been completely wet.
Factual error: At the end of the movie, after losing the 1954 Boston marathon, Father Hibbert asks Ralph what his running plans are for the future. Ralph replies that the Olympics are next year and he plans on winning them. The next Olympics were in 1956, not 1955.