Hi
It's got to be with Therodore Bikel,how the Lt entices the baddy to re-enact the crime for him.Also not forgetting showing the baddy he is wearing gloves in "Suitable for Framing".
I haven't got series 4 yet but hope to soon,The mind game with Bill Shatner as the TV detective must count as one of columbo's best goals, also not forgetting the mind game with Robert Conrad.I was quite surprised to see so much interest in a detective for so long.Am i an anorak or what ?

Based on the literal question you raised, how about his literal answer to Faye Dunaway in "It's All in the Game".

Can you solve this case without a confession lieutenant?

Not only does he say NO, but he portrays a frustrated downcast countenance.

Isn't it also in "All In The Game" that the murderess asks Columbo how long it took him to solve his most difficult case. Columbo responds something like, "14 years."

This would make "interesting nod to the viewer" sense if it had been 14 years between "The Conspirators" and "Columbo Goes To The Guillotine". But it wasn't actually that long a period of time.

In terms of sheer leg-work..I think How to Dial a Murder was a pretty tough assignment.
Columbo had to go out to that ghost town, visit laurel and hardy when they were confined, visit the animal trainer where he had to stay up all night long..and all the while had to deal with Dr. Mason's mind games..figuratively and literally.
And to top it all off he had to possibly risk his own life...what if the animal trainer's reversal of the dogs hadn't worked correctly.

I find it odd that in "A Friend in Deed" that Columbo
doesn't resist more the idea that the Deputy Police Commissioner did it. I would think that he would find it incredible, but he glomms onto him just like the other suspects.

I think right from the get-go Columbo had all these little things as usual that bothered him and the Super was too sure of the burglar accusations.

I always thought he came close with Johhny Cash. Cash had it in the bag, he was on that flight and away...