I'll try anyway!!
What similar thing happens in each of these episodes? (Hopefully I won't screw this up!! )

Ransom for a Dead Man
Murder By the Book
Death Lends a Hand
Dead Weight
Blueprint for Murder
Dagger of the Mind
Double Shock
Any Old Port in a Storm
Mind Over Mayhem
A Friend in Deed
An Excercise in Fatality
Last Salute to the Commodore

It sort of happens in Etude in Black, but not exactly.

This "thing" that happens is sometimes on camera and sometimes off.

Good question - I was working along the lines of the murderer re-visting the crime in this head, which we get to see on screen...sometimes when Columbo first arrives at the murder scene and is questioning them..

Then, I thought no. Has it got something to do with the identification of the body by murderer or relative at the morgue....?

Perhaps not...when are you going to put us out of our misery?

Well, since I only posted this yesterday, I think I am going to have to let you squirm just a little bit longer. Sorry.

I will just say that the similar thing has to do with the dead body.

After the murder, the killer moves the body.

PAUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

TERRIFIC!!!!!!!!! You Dun Good Kid!!!!

Just one clarification. In A Friend in Deed it isn't the murderer (Halperin) who carries the body, but Hugh Caldwell. But I included it because my exact connection was "The body is picked up and moved to another location." I wasn't going to add in the fact that it was the murderer.
And as far as Etude is concerned, Jennifer Welles was not dead yet when Alex carries her to the kitchen.

I am so proud of you Paul!!

Awww, I didn't get a chance to play.

Awwww.....well you know you would have gotten it anyway...and you would have given your normal (and wonderful!!) cryptic answer!!

So, Headache, did I do sorta good? Please tell me I did!! Just lie!!!

Sincerely,
Headache Jr.

Cassa, you did (ahem!) sorta good.

Naw, actually, you done real good!

Thanks Bud!!!