The Hoodlum - S4-E1
Factual error: Diamond's car phone, quite a rarity in the 1950s, attracts a lot of attention. But the car should have a huge antenna attached to make the gadget work (it doesn't), and Diamond would not be getting direct calls - they'd have to go through a mobile operator first.
Visible crew/equipment: Just after Danzig throws the wrench at Diamond, the boom mike dips into the shot at the upper left of the screen.
Visible crew/equipment: As the landlord is unlocking the apartment door for Diamond and the cops, the camera shadow is visible at the lower right of the shot.
Visible crew/equipment: After Diamond warns Mrs. Porter about defrauding the insurance company, an equipment shadow moves on the wall behind him.
Continuity mistake: Diamond is backing his convertible up to drive away from the crime scene. He turns to look behind him and places his right arm on the top of the seat. When the shot cuts to a wider angle, his arm is suddenly in a different position, draped all the way over the back of the seat.
Continuity mistake: When Diamond pulls his car up across the street from Sutro & Son, the building behind him is in shadow. In the next shot, as he parks, it's in bright sunlight. When he gets out and crosses the street, the shadows are back.
The Fine Art of Murder - S4-E16
Continuity mistake: Diamond comes in to an alley and sits up in front of a white crate. When the angle changes, he sits up again, and now the crate behind him is black.
Revealing mistake: When Diamond is driving with Ted, his wife and their dog in his convertible, the rear-view mirror, which was there earlier, is missing. The shaky rear-screen projection makes it even more obvious that the car is a studio mock-up with the mirror removed to make the actors' faces more visible.
Continuity mistake: The bad guy backhands Ted, striking him across the right side of his face. Later, when Diamond questions him, Ted has bruises on the left side of his face.
Visible crew/equipment: While the gangsters are forcing the bar owner to buy their liquor, the boom shadow moves across the top of the shipping crates.
And Whose Little Baby Are You? - S4-E18
Audio problem: When Diamond and his date are entering his apartment and he says, "You never know," his lips aren't moving with the words. (00:03:00)
And Whose Little Baby Are You? - S4-E18
Revealing mistake: The $100 bills Diamond picks up from the table are very obviously not real. The stage money's rather frilly design pattern looks vaguely like some currency from the 19th Century, but it doesn't resemble anything in circulation in the 1950s. (00:06:30)
Fallen Star - S4-E19
Continuity mistake: Diamond takes a full cup of coffee from the vending machine and walks down the corridor with it as he talks to Mark. He takes only three brief sips from the cup before turning to leave. There are no time gaps in the scene, nor is there anywhere for him to have poured the coffee out, yet he tosses an empty cup into the trash on his way out the door.
Continuity mistake: The hitman fires at Diamond and the bullet strikes a post beside his parked car. In the next shot, as Diamond races into the alley after the gunman, the car is in the background, but the post has disappeared.