Other mistake: The shopkeeper hands Danny a Beretta 92fs/M9 handgun with a detached suppressor. To mount a suppressor to the muzzle end of the handgun the barrel needs to be threaded, and this one isn't. Sometimes barrels are threaded and when no suppressor is attached they are protected by a thread barrel cap to protect the threads from dings and bumps. There is no thread cap here either. (00:22:35)
Other mistake: The woodchipper is shown cutting wood, but is squeaky clean when the golfer sticks his hand in it to get the ball out.
Episode #1.3 - S1-E3
Other mistake: After the arrest of "ABC" and a brief scene with the interview to Betty's family, there's a prolonged close-up of a newspaper with the date "24 April 1933." Besides the article on the serial killer, there's a headline that says "German ministers in Rome - Uproar as Strong Arm men pack benches." The body of the article though talks about the Persian parlament, and the prime minister mentioned is "Dr. Mossadeg." Mohammad Mossadegh's public office as PM and his visit in the US mentioned in the article happened in the 50s.
Other mistake: The opening scene shows a captive with a hood over his head being dragged barefoot along a long driveway by two men. His feet are dragging over the ground. He is then strung up by his hands, and when they show his feet, there is not a scratch on them.
Undisclosed - S2-E7
Other mistake: Toward the end of the episode the perpetrator is corned by the FBI. He steps backwards from the curb and is killed instantly by a garage truck moving at a high rate of speed. In the following scene the garbage truck is shown just a few steps beyond the scene just behind a parked car. The truck was going very fast when it killed the perp and could not have stopped so quickly. Further it would not have been going that fast in a curb lane with a parked vehicle right ahead of it.