Factual error: The armed robbery is reported by the radio call as happening in "4014 Nostrand Avenue", which is a real street in Brooklyn. However, the first detectives to respond to the dispatch identify themselves as being from "Manhattan South" (makes sense, Kojak being a Lieutenant of the fictional 11th Manhattan South precinct), and the rest of the episode is set obviously in Manhattan. That's many miles away.
Beyond the Farthest Star - S1-E1
Continuity mistake: There is an alien in a Starfleet gold shirt sitting next to Sulu. For a second, there is a human in a Starfleet red shirt, then it goes back to the gold shirt alien.
A Community of Victims - S3-E3
Continuity mistake: Officer Ripley's shoes change from black to white as he chases the ambulance, then back to black.