In the early scene where John Moore is being taken to the murder site, he passes by an elevated train which has doors in the interior of the car. The elevated train cars at the time had no doors; passengers entered and exited from gates at each end of the car.
The opening credits of every episode show various familiar New York landmarks built after the show's 1896 setting being unbuilt in reverse time-lapse, to convey the journey back into the past. However, the final landmark shown being disassembled is the Statue of Liberty, which was completed and dedicated in 1886, ten years before the show is set.
When Laszlo and John meet Sarah, she is in the police station, typing. The speed at which she types and the accompanying sound is impossible on the type of typewriter she is using. They were loud, clunky machines that do not lend themselves to speed-typing.