I expect there will be two conversations going on: one about the book, and another about the mystery discussed in the book. To stick with the book for now, here's what I prepared when I finished reading it...
I think it was an interesting idea for a book published in 1951, and was reasonably well handled considering the constraints (book length, audience expectation and so on). As such the book earns about a 3/5 from me: worth reading but unlikely to ever revisit. I do have trouble working out how it came to get voted into all-time best lists ... but then the book faces a big hurdle with me: I detest Inspector Alan Grant.
Please excuse what follows, especially the length, I need to get this off my chest and then maybe I can talk about the book more calmly. (Some parts in spoilers to make it look shorter.

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Dear Alan Grant, how do I loath thee? Let me count the ways. Here is a small selection of quotes that, to my mind, mark him as a smug, self-satisfied and arrogant son of a ... Scotsman:
Grant's name calling isn't humorous, it's derogatory. He's
always looking down his nose at everyone else (although perhaps not Marta). At best he's condescending, but much of the time I think he's worse than that.
Plus there is his major offence: “I see that you have managed to read at least one of the books I brought you—if the rumpled jacket is any criterion.” A rumpled book jacket! No trial is needed, put him up against the wall. Now. We won't bother waiting for dawn.
And to top it all off, he's just not that smart.
It is possible to have dislikeable detectives and still have it work. I never particularly liked Christie's Poirot, but she sensibly makes him a figure of some ridicule so that the audience has reason to feel superior while still admiring his "little grey cells". Tey's Grant is all arrogance and self-satisfaction while also being outright wrong about so many things as to seem just silly, but this is never acknowledged by the characters or the author; they don't seem to see it.
I might have had more patience, but the first book (
The Man in the Queue) was a did-not-finish for me a few months ago, and for all the same sorts of offences.