Continuity mistake: When James Dean's mom writes out a check for $5000 and gives it to him, she licks the envelope first, but when she actually hands over the envelope to him, it's clearly not sealed.
Suggested correction: I noticed this, too, but as it's all one shot, it's not a continuity error; it's simply that she didn't properly seal the envelope. Not a film mistake.
Factual error: The opening scenes in 1918 Monterey show a US flag with 50 stars, and clothes inappropriate for the period.
Suggested correction: The flag shown has 48-stars. Even though I verified it by watching the scene, I know it would be impossible to have 50-stars since there were only 48 US States in 1955. And nothing about the clothing seems "inappropriate."