Love your analyses. A couple of particular points which struck me -
(1) The 'security' cop (played by Ed Begley). Spot on. It always bothers me when he walks out, "Lemme check with Lt. Columbo, I think he's around here somewhere." Really? Walks out of a room where nobody is allowed to see the dogs. On top of that - it's kind of strange that Columbo is actually at the police station! He's never at the police station. As he said in "Forgotten Lady", "None of the murders happen there."
(2) The tape recorder. I never noticed this in Columbo's pocket either until a decade or so ago. It's an elegantly filmed scene, which fits in so nicely with the overall moodiness of this, in my opinion, terrific episode. It has many elements of a motion picture and not just a TV show, this scene being one of them.
(3). The chocolate. What bothers me is that Columbo, who's been charged with protecting the dogs, doesn't say anything when Dr. Mason says, "Even chocolate?" According to this article: https://vcahospitals.com/know-your-pet/chocolate-poisoning-in-dogs. the chocolate doesn't poison humans but it does damage dogs due to their inability to process the theobromine and caffeine contained in chocolate. I would have thought Columbo, a dog owner himself, would have known chocolate would be bad for dogs. A more appropriate response from Columbo would have been,
"Dr. Mason, I'm surprised you would want your dogs to have chocolate. That's very bad for them."
"Lt, I didn't know you were an expert on dogs."
"Oh, yes, sir. I have a dog. He's a low-slung model, certainly not as smart and well-trained as your dogs."
(4) "ROSEBUD" - yes, the dogs were conditioned to attack on this word. This was their 'Kill" word. The phone ringing was conditioned to get their attention and bring them to a certain spot (the kitchen phone in this case). Once alerted and in position, they were then given the kill command and would attack whoever/whatever was there. In Dr. Mason's kitchen that was originally the dummy Charlie stuffed with straw and scented by the vest. In the murder, Charlie himself was there at the phone and had to say, "ROSEBUD" in order to trigger the kill. By the pool table, Dr. Mason already had the target (Columbo) present, so he simply had to say "ROSEBUD" and point at Columbo.
Maybe it's the point, but it's funny how Eric lectures his clients about being in control, but he thinks has to murder his best friend, and maybe his wife. Even if it is because of their affair, that isn't exactly being in control.
Since he's a psychiatrist, he needs to "own those feelings" instead of murdering people.
I don't think Mason intends to kill his dogs. That is simply the impression of the viewer, because of the sinister character and the atmosphere of the scene. Besides, that would only accuse him (his visit would be registered) and they are going to be sacrificed by court order. On the other hand, chocolate is bad, but not lethal for dogs. I doubt that the health argument would have been taken into account (for example, in "Anatomy of a Murder", the dog drinks beer and nobody was shocked).
Of course he intends to kill them. Mason says, "I'd like to wish you two a long and healthy life, but that wouldn't be so good for me. So, you're going to have to do me one more favor."
As I've said before, killing them would only incriminate him. For me, that "one more favor" is to be sacrificated, what would happened in a few days. But the scene of the visit seeks to produce tension in the viewer and succeeds in doing so.