In the scene where Ginger asks Melvin for his fish, he takes a coke out of his back pocket and opens it. There is no sound of it opening. Also in several different jump cuts of this scene the coke can changes back and forth.
After Ginger moves into her flat she starts cleaning and puts books on the shelf. The spines are facing the camera when she puts them on the shelf. In the very next scene when she is dusting the books have turned around.
(at around 26 mins) When Mel visits Diana's apartment for the first time, the door falls shut after she opens it for him. The sound of a door shutting can be heard, but in the mirror to the left you can see that Mel caught the door before it closed so there should have been no sound.