Revealing mistake: When Lizzie awakens on the morning that Edith gets released, Edith doesn't respond and Lizzie goes to her bed to "mourn" the passing of her friend. Except that Edith is still breathing.
Deliberate mistake: After MacNelly enters the ladies room to confront the red haired lady, she shoots the woman in the chest, but there's no gunshot or bullet hole or blood anywhere. But the red haired lady dramatically collapses to the floor. Then during a closeup, glances upward at MacNelly, and then her head droops downward.
Revealing mistake: For a prison governor/warden, Mrs. Davidson (Erica) would presumably earn a modest upper middle class salary. Yet here she is on the phone, in the foyer of her home, wearing an elaborate house dress, surrounded by very stellar furnishings. But then she answers a knock at the door, and opens it to reveal a very ugly vertical striped wall mere feet behind her visitor. Obviously indicating that she either lives in a dim-tenant or low-scale apartment, or this scene was shot in-studio.