In the golf sequence, one of the five golf balls thrown on the solid base has rolled off onto the grass. After Fred has hit the first four balls, the camera cuts to a new angle and the last ball has moved from the grass to the solid base.
At breakfast after the dream sequence, the position of Amanda's hand holding the glass changes between shots.
While Amanda and the judge are firing shotguns at the range, neither are wearing ear protection. However, this was not a concern at the time this film was made - in 1938 - as it would be decades later.
At the end of the first brief dance at the dinner party, the music slows to a conclusion, but the conductor continues to move his arms as though the music is still playing.
As Amanda (Ginger Rogers) exits the taxicab and starts to cross the street for the theatre, you can see the reflection of the roof line behind her in the large piece of plate glass on the truck. On the roof line, you can see the rigging pipes for lights and other equipment showing it's a back lot set.