In Death Lends a Hand, He suspects Brimmer very quick due to the ring he was wearing when he read his palm. As a side note, I found Brimmer to be a real pompous idiot thinking to himself "You'll never think I was the one who did it."

I think that every episode that follows the Columbo “formula” has some evidence that “bothers” the Lieutenant early on. Why was the other car washed and waxed and not the one Senor Montoya would normally drive? Why did Mr Van Wick write the phone number down when he normally has the security guard write it? “I’m sure it means nothing”, but to Columbo, it ALWAYS means something.

Why did Dr. Keppel have the presence of mind to return the film to the vault but still leave the tape machine running?

From the very first episode: Why didn’t Dr. Flemming call out to his wife when he returned home?

And from the last: What took so long for Justin to answer his beeper?

It’s just a question for the report of course. Just Columbo’s superiors making him ask all of these stupid questions as a formality. The new boss is a good guy but a little young for the job, etc. lol.

It's always bothered me a little that right after meeting Abigail Mitchell, he tells her that he doubts Edmund's death was an accident. Do I keep missing something or do you ever find out why he doubts that immediately?
And either way, why would he say that to someone who might be the killer?

Coming upon the scene as a detective (or an observer), one would suppose that it was purposeful (that he got locked in the safe). Because there is no other viable explanation of how it happened. (When Abigail later provides an explanation to consider, it is quite weak -- and she mixes it with her explaining to Columbo that she called Addie to turn the alarm back on because she forgot; a certain eyebrow raiser, especially given that she earlier plead confusion when Columbo put the question about the alarm to her and he said, "Oh, I can't really imagine you confused, Miss Mitchell."

Sharing the information (that it is not deemed an accident [because it very much looks purposeful]) with anyone is not only not a problem, it is valuable in rapid establishment of the case AND it is simply a conveyance of the situation as it very much appears. Here it may be considered the second move of this chess game; Abigail's mention of it as an accident being the first. Her forthright attempt to cast it as an accident is immediately met by Columbo's reply, which, reactionary, calculated, or otherwise, seizes the initiative. Abigail is thrown for a loss here, from which she never recovers and only slides in deeper, as evidenced in the conversation about the alarm switch and the later disclosure of her calling in to get the switch switched.