The siren speaker on the police car is a Federal Signals electronic speaker that was not introduced on police cars until the mid-'60s. Sirens of the era of this movie would've been electro-mechanical wind sirens.
The diesel locomotive pulling the train that Pete is riding back to Lawson near the end of the movie is a later model Electro Motive Division GP (general purpose) engine that was not available until the mid-60s. Diesel engines were certainly available in the early-1950s, but not that model.
When Harry and Peter are in the auditorium of Majestic together for the first time and Harry is explaining the Majestic to Peter, Harry's shirt collar changes from being inside of his sweater to outside of it between shots.
Before Pete's car goes off the bridge, the front end is hanging off the edge of the bridge angled downwards towards the water. But a brief reverse angle shot shows the car's rear end hanging off the edge of the bridge, with the headlights angled up towards the sky.
When Luke picks up Adele for the "Welcome Home" dance, she is revealed in a beautiful red lace dress, with a small necklace that has red stone pendant. After they arrive, and begin the first dance, a close up reveals that Adele is wearing a metal locket instead.
When Pete wakes up from the car crash on the beach it is early morning and the sun is shining but as he walks on the beach his shadow falls on the east, away from the sea, indicating the sun is in the western sky. In California, that only happens in late evening.