Continuity: During the conversation with Marty, Angie and their friends about how Mickey Spillane writes women, Marty's shirt is alternately unbuttoned/buttoned between shots.
Revealing mistakes: When Marty and Clara are walking on the street on Saturday night, a woman approaches a "No Parking" sign, turns and waves to the camera.
Continuity: In the first scene, when Marty is talking to Mrs. Fazarri in the butcher shop, in a frontal shot of Marty he is slicing pork chops and puts the knife back, and begins to wipe his hands. When the camera angle changes to a rear shot of Marty, he is again slicing before putting the knife up to wipe his hands.
Continuity: The amount of Coke in Marty's glass changes between shots.
Factual errors: The opening scene shows men in a bar in the middle of the afternoon. One patron says that the Yankees won both games of a double header that day. However, even in the 1950s games took about 2.5 hours to play so it is unlikely that a double header would have been finished by mid-afternoon when the scene is set.
Errors made by characters (possibly deliberate errors by the filmmakers): When Marty rushes into the street to hail a cab after taking Clara home, he ends up facing the camera on the near side of the street, waving for a taxi while facing away from the oncoming traffic.