"Why the surgeon would put that where the patients would see it I cannot imagine."

Maybe the same reason people in doctors' waiting rooms seem to want to have conversations with each other about medical stuff, whatever that reason is. When I say that, I don't mean urgent talk about medical things, I mean the very casual kind. You'd think that in a doctor's waiting room they'd prefer to talk about anything else!

Oh, that's easy. He wants his patients to recall how "bloody hard" he and his team worked to save their lives. That way when they get his bill, they won't be too upset.

Thank you for the anecdote and its relation to "A Stitch in Crime." That was one sterile operating room when you compare it to real life.

Now that I've just watched "Ransom for a Dead Man," I can now contribute an alternative explanation.

In that episode, Leslie Williams shoots her husband in their own living room, then wraps up his body, drags it to his car, and disposes of it. Columbo explains the oddity of the total absence of blood evidence by noting that Williams was shot with a .22 calibre hand gun. He asserts that Leslie specifically chose that calibre because those bullets do not have the force to exit the body. They would simply remain lodged in the body's tissues.

So maybe all these bloodless victims were likewise killed with .22 calibre guns (?)

On the other hand... I'm no blood spatter expert, so I can only surmise; but when a bullet penetrates the body, wouldn't you expect that some blood would leak out from the entrance wound? (... unless the bullet itself stanches the flow).

It is briefly mentioned in Dawidziak's "The Columbo Phile" (a wonderful book but sadly out of print and hard to find nowadays) as "an important step" for the show that while the strangling of Carol Fleming was gruesomely played out before the camera in "Prescription: Murder", later episodes (starting from "Ransom For a Dead Man") would either not show the murder at all or show it in a "sanitized" way. Obviously this was an intentional choice by the producers.

Of course, all those bloodless murders aren't exactly realistic, but it has never bothered me. "Columbo" is not about realism anyway...