The part I found extra entertaining is that they were often exploring the dynamics and politics of different artistic industries.

Books, museums, the art world, burlesque, comics, radio, tv, etc. The murder would happen in one of those spaces and then the show would explore the politics and how things functioned.

The flaws of the era were still there, but they were definitely trying to be thoughtful and open up the conversation and show the humanity.

I'm guessing if there was any validity to the idea of a "death clue" we'd still be using the idea today.

There was also a point in every episode where the lead would break the fourth wall and ask the audience if they'd figured it out and run through the list of suspects.

Which was an interesting way to engage the audience, but there is no way you'd guess the outcome based on the information actually provided. It was typically some random left turn detail that you wouldn't just guess.

There were rich, unhappy marriages, mistresses and affairs and they still treated them like normal people. Those things did not automatically mean "the killer."

And the show was a who's who of classic performers. I saw Betty White, Eva Gabor, Donald O'Connor, Vincent Price, and even a George Burns cameo. And those were just the faces I knew the names for.

Unique conventions:
They were big on this "death clue" concept. Where the victim would try to grab some item that indicated the killer.

For instance, I love Natalie Wood and even really like the original West Side Story, and totally brownface.

What impressed me is that the story was set in 1947, and they went out of their way to represent a variety of immigrants and experiences of the war. And even when those characters were implicated in the murder, their stories were very human and it was typically some rich, conspiring white person setting them up.

They also went out of their way to represent non sugar coated relationships

It was interesting, because they legit cast Black people in respectful and representative roles, though they were still regularly incidental characters.

Seems like they broke out the brownface for more international characters. The blatant one was East Indian (technically the only actual Indian, but clarity), and it may have also happened with an Egyptian character and a South American couple

Hollywood had a blind spot for slapping on some make up and thinking that was enough for a long while

I am now going to deconstruct the storytelling and era, like a good little nerd.
I am not in any way claiming context takes away potential offense. Our country has been offensive a damn while, but I think this show was legitimately trying to be thoughtful and representative, while still having some typical blind spots of the day.
I am NOT the arbiter of offense. Just a nerd for contextual deconstruction.

There was definitely some brownface happening. But it wasn't in any way minstrel stuff.