In this 1968 two hour Pilot, (about 1hr-34min in), Columbo is waiting for the suspect's lover to approach him at the movie studio. The long shot, from behind and above Columbo, shows him standing next to the ice cream truck, and placing his briefcase on the ground, to the left and front of him. A tight-shot from Columbo's front, now shows the briefcase tight and to his left leg, while Columbo rips the wrapper from his Popsicle, and he THROWS the wrapper to the ground behind him. The next shot is again the long shot from behind and above Columbo. His briefcase is now, again, to his left and in front of him, and there is no sign of the Popsicle wrapper which he just threw on the ground behind him.
A few episodes have the murderer firing a silenced gun without any close by character hearing it. A silencer does not muffle the noise completely, as it can still be heard by someone nearby. (This is a common mistake in TV and films).
Columbo often undertakes actions which would result in evidence and investigations being compromised, these actions could result in cases being dropped or overturned upon appeal. There is no way that the District Attorney would allow Columbo to perform the actions that he does in the show.
The description of the 'Mrs. Columbo' character is not fully consistent with details from the mentions of her in many episodes.
There can be a few plot holes realized in certain episodes. With the way the murderer is covering up the murder and how Columbo figures it out.
In multiple episodes Columbo manages to get a "confession" of his murder suspect in his house, and proceeds to tell him how he found out the truth. Neither of these facts are sufficient for prosecution and it would be a gross violation of police procedure to reveal the evidence against the suspect outside official police interrogation and possible plea deal.