During Fay's musical number in the club, when the camera is focused on Johnny in the foreground, Marlene Dietrich's lips in the background do not match the song. Most of the time, she appears to just be sitting in the background and not even singing.
After Johnny bails Fay out of jail, they are seen walking together down a stairway at the police station. When they arrive at the first landing, as they turn and continue to descend the stairs, the shadow of the microphone boom can be seen on the wall behind them.