absolutely, those little moments make the show very enjoyable to watch.
One of my favorites is in Prescription Murder, at the very end when the killer realizes Columbo's trick, he looks over at Columbo and Columbo gives him a look that I don't even know how to describe, but it's perfect.
There's no one thing that keeps me interested. It's a combination of things. Speaking primarily of the early episodes:
Terrific plots.
The singular atmosphere of the 70's.
The Americana.
The truly 'lived in' feel and contrast between scenery, from upscale and regal to the dark and gritty.
Realistic dialogue and nuanced performances from a variety of intriguing characters.
The warmer picture quality and cinematography.
The soundtracks.
And of course the man himself, Peter Falk.