Continuity: There is an error in the scene where Dave is drafting behind the Cinzano truck. In the second close up shot of his legs (cranks) pedaling the bike he is in a lower (easier) gear than the previous shot even though he is supposed to be riding significantly faster.
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Mistakes
At the end of the scene when Dave races with the Italians, the bike he is riding when the Italian puts a pump in his spokes is not his bike. His bike has a chrome plated fork crown, and brazed on shifters. The crashed bike is a cheaper bike with a cheap fork that has no chrome, has paint missing on the inside of the right fork blade, and the bike has clamped on shifters. See more...
Breaking Away mistakes
Continuity: In the climactic race scene near the end, every time the camera cuts back to a long shot of the race, the lap number on the board goes up and down, rather than going up sequentially.
Continuity: In one of the shots where Dave Stoller is chasing after the girl to return her notebook, we see him riding his bike in front of a building. In the next shot he is riding in front of the same building, going in the other direction.