Continuity: The "newest battleship" that the Nazis want to sink is either the old "Nevada" or the old "Oklahoma", both built during WWI.
Continuity: Gloves' pistol is visible before he draws it from his coat.
Continuity: The slice of cheesecake shrinks as it is brought from the kitchen to the table.
Continuity: 16 minutes into the movie, Gloves is sitting in an armchair. A glass is on the arm and it is clearly visible when the phone is brought to him. The edge of the glass is visible at the bottom of the screen through the phone call, but when Gloves stands up and the phone is brought away, the glass is no longer there.
Continuity: Around the 64 minute mark. Bogart's car has been shot at and has spun out. The first scene shows everyone getting out of the car, next we see the inside of the other car, and then we see (from the side) everyone getting out of his car again.