Just noticed, after discovering the phones were bugged and they arrive at the house to listen to the tapes with the Lawyer Columbo mentions the Ice Cream trucks work the Stadium, Columbo says it's crucial we determine you were at the stadium at the time of the murder... Phone records.. why, like they do in any other episode, don't they check the phone records? The last call the Kid got would have shown it came from a nearby phone booth... No?

There were several weak links in this episode. The fresh water on the deck not evaporating; the weak 'gotcha'. When Hanlon claims he called Eric twice from the box, Columbo says, "Unfortunately, the telephone company's records can't prove that." So, Columbo did look into it. I don't know the exact methodology of checking phone records in Los Angeles back in 1972, but I think I've seen an article about this somewhere. For the purposes of the Columboverse, let's assume he did check them, as was indicated in the show. If that's true, then, as Hanlon said, "That's not MY problem."

At the other extreme, there are such accurate phone records in "Double Shock."
And of course, that's in Los Angeles, and 1972-73.

I would give the writers a pass on the phone records.

Back then, there were only phone records of long-distance calls for which there was a fee; Even within the same area-code a call could be considered "long-distance", but not as costly as outside the area-code.

The brothers in "Double shock" could live far enough apart to be a long distance call.

In "Crucial Game", the phone-booth to house call would not have been long-distance and would not have been logged. As for "the phone company can't verify that", the lack of a logged toll gives Columbo sus.picion but of course you can't PROVE he didn't call just because the call wasn't logged. In a court of law you could always just blame it on a phone-company error, and that's plenty of reasonable doubt.