While I'm typically not that interested in so-called "dark" themes in television and film (it usually seems very forced and mellow-dramatic to me), there are several "Columbo" episodes that stand out to me as being particularly sinister in tone, and succeeding in it wonderfully.

For me, "How To Dial A Murder" represents the height of malevolence in the series, both in the murderer's character and the overall style of the episode. Though there are a couple of Eric Mason's lines I feel are delivered sort of blandly by Nicol Williamson,generally I think he was brilliant as a murderer who was at the same time both broadly drawn as an "evil mastermind"-sort and subtly nuanced as a genuine neurotic.
Two scenes (among several others) that I feel encapsulate the darker tone of the episode is the introduction of Dr.Mason, as he relentlessly hammers away at his lecture audience with his eccentric brand of self-help ("We don't want you contaminating each other with your nasty little fears and insecurities. And if you don't think you're that kind of a girl or that kind of a boy...etc"; "They took control with the control words! Then the words took control! Now who's got the control? I'VE got the control!") and the scene where Mason is fiendishly "consoling" his dogs before trying to kill them (I wish you a long and happy life, but that wouldn't be so good for me...").
Aside from that, the music in the episode is absolutely dreadful, in a good, effective way, of course.

Other episodes I feel have this sort of "edginess" are "A Friend In Deed" (e.g. the scene between Halperin and Caldwell in the funeral home; Halperin's devilishly mocking response to Caldwell's concerns about not using anymore violence in their scheme etc); "Make Me A Perfect Murder" (as with "Dial", I think James Frawley creates a stylishly grim atmosphere here, too); "Old Fashioned Murder" etc.

Are there any episodes, or specific scenes, that stand out to anyone as having this sort of "dark" tone?

I think you are entirely colorectal in what you chose as a dark episode. It was particularly grizzly when he smiles as his dogs tear apart his erstwhile friend. Also loved seeing a very young Kim Cattrel in that episode.

I meant "correct", not "colorectal" LOL

I agree with you completely. There is not a thing to like about the two murderers you mentioned. In some other episodes the murders have a 'decent side' but not those two. Credit to the actors and writers for creating such dark characters.

I feel funny bringing it up this week for the obvious reason, but there's another very dark moment in A FRIEND IN DEED. It's when Mark Halperin pretends to be desperately trying to give Margaret mouth-to-mouth, knowing she isn't alive!