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.