Factual error: Probably an in joke - the wheels of the "airliner" shown landing at LA international airport are those of a B52 bomber. They are very distinctive and look nothing like those on any airliner ever made.
Factual error: In the middle of summer in southern California, water spread thinly on an outdoor ceramic surface would start evaporating immediately and would be gone in about fifteen minutes. The surrounds of the pool would be bone dry by the time Columbo arrived at the scene, nearly an hour after the murderer sprayed the water there.
Plot hole: In the last scene Columbo convicts Hanlon of murder by playing back the recording of Hanlon's final call to the victim Wagner (the phone-box call near the crime scene is Hanlon's alibi. He is pretending to be in his VIP-box in the football stadium, which is too far away at the time he murders Wagner). The point is that the recording is missing the loud clock chimes from a little clock inside the VIP-box, which means Hanlon's alibi is "destroyed", he was not in his VIP-box, he must be somewhere else at that moment. Problem is the missing clock chimes are not hard evidence. Hanlon could say the clock was not working that day or the battery was empty and so on. Beside that it would be much easier to catch Hanlon if Columbo would check the outgoing phone calls asking the telephone company.
Suggested correction: He very likely will. As we've seen, Columbo is very thorough. The missing clock chimes aren't meant to be definitive proof, just enough to warrant an arrest. Columbo will continue to work the case and gather evidence.
Columbo will continue to work the case and gather evidence? Well with that sentence they could stop every Columbo episode after 5 minutes. Hey guys, Columbo has nearly nothing against the murderer but he will continue to work the case outside this episode be sure.
It's the detective's job to investigate the crime and gather sufficient evidence to warrant an arrest and potential conviction. Yes, this would apply to every episode, and yes it applies to all detectives. Many of Columbo's investigations result in him using circumstantial evidence to arrest the killer. In one episode he arrests a man based on how the victim's shoes were tied. That wasn't his only evidence, however. In many cases a preponderance of circumstantial evidence is enough.
It's a TV show, Columbo was made for entertainment, not to be used as a script to prosecute a potential criminal.
No judge would allow this "evidence" to even be presented to a grand jury. Just because Hanlon wasn't in his booth at the time doesn't mean he was at the murder scene.