My favorite part (it's all funny), just as a Columbo history buff, is when he reveals Mrs Columbo's first name.
(Well technically, it's not part of the canon, since it was said by Columbo but not in "Columbo". Even so, it's intersting, and a good fit.)
Believe it or not, several years ago Peter Falk was reminded of this appearance by seeing part of it on this web site (see the Scrapbook article, "Columbo and Sinatra") and, through his producer, Peter asked me for a copy of the tape. Of course, I agreed and sent him a copy. He got a big kick out of re-living the experience, and after watching the tape, he commented that he had completely forgotten about how he broke one of his own rules by revealing Mrs Columbo's name.