I think the reason for the ash on Oliver's face is because he pushed the umbrella (squibs and all) up the chimney. Then he relaxed because the "hard part" of the murder was done and that's when he saw that chimney soot was on his face. That would clue the police to look up the chimney. That's how I saw it anyway.
I think the 20,000 members obviously don't represent the top 2% in IQ. There are many who are in the top who don't want to be in the Sigma Society (or Mensa).
I agree that the wife was unattractive, but mainly because of her personality. Oliver is confessing embezzlement and she doesn't care. His best friend died and she wants to go on vacation: "But darling we're alive!" She doesn't come off as being very compassionate.
I like the episode though. Some people put it at the very top, but, like Matti, I don't find Oliver sympathetic. He picks on his friend Bertie. He embezzles rather than tell his wife to take a hike. He belittles and threatens an employee for no reason. It's hard to feel bad for him.
I disagree about the wife, in the sense I think she's good looking, however not a very good person obviously with the reaction to bertie's death or "not wanting to understand" oliver's embezzling problems, and for this reason I liked his answer in the end (keep in mind I watched all columbo episodes in italian, so words might differ a little in the english version): she asks him to come home to bed with her and that she needs him, and he answers "unfortunately I doubt I'll need you any more... for a while" and hangs up.
I also don't find those compliments columbo made creepy, on either episodes.
Indeed, the monologue about the umbrella was strange and I'm guessing it made him even more suspect in columbo's eyes, also agree that for a genius he didn't make it difficult for columbo to catch him.
Lastly, I don't think the sigma members are stupid, just eccentric, which oliver says as well; the president danziger in particular, and I liked the ending, when oliver calls them stupid or something along the lines: columbo answers: "the president danziger, you can't call him stupid", "why?", "cause the idea of the book was his, vibrations" "vibrations? What are you talking about?" "of the first squib that exploded, he explained it to me in the easiest way: when the squib exploded it provoked some vibrations and that's right what made the dictionary fall! That danziger's a genius!", and then ofc brandt incriminates himself; columbo knew this theory was crazy and gave danziger credit for it, and brandt couldn't stand that and that's what led to his fatal mistake!
Overall, it's one of my favourite episodes, I also liked that problem with the sacks of gold.
You did such a great job of describing the ending of the episode that I could almost hear Tcaichovski playing as the veins in Oliver's forehead bulged out, lol.
And yes, the wife is physically attractive, but what a nightmare for a life partner. As evil as Oliver is, he embezzled and killed Bertie to keep HER happy, and she won't even let him finish his sentence.