Factual error: At the crime scene, the landlady of the dead man is brought into the room in order to identify one of the dead men. This is never, ever done - she could contaminate the crime scene in a dozen different ways. She would be asked to identify the corpse at the morgue after the scene had been cleared by forensic examiners.
Factual error: Despite the fact that other officers are doing so, Columbo does not wear gloves while examining the crime scene. He also eats and drinks in the room - both absolutely forbidden - leaving eggshells scattered about the place. The crime scene is now totally compromised and nothing found can be used as evidence.
Other mistake: Fielding Chase and Lieutenant Columbo are on a road in the mountains above Malibu and Chase's car will not start. He tries unsuccessfully to call the Automobile Club on his mobile phone. He tells Columbo the phone number is "555-4411" but each time he tries to call, he presses nine digits.