The rarity about this show is that every now and then it isn't the main character doing it. There has been about five percent of the shows where Beckett alone closes the cases, but I don't find them satisfying, maybe because I expect her to. And If I remember correctly, sometimes they have tried for her to have creative flourishes at nailing a suspect, and that's fine character-wise, maybe, but it's too similar to what Castle would offer. I would expect from her something that it's on its face more the type of easy solution a cop would see, but that feels fresh because of the context. (Say, a lot of wild speculation thrown in beforehand, f.i.) 

As for Closing Clues, I like the comic-book episode one, even if it's in reality an impossible one. (The coat on the wife being the missing piece for the ID the deranged Morlock gave about the killer) and how he cleverly maneuvered her to be confronted by the jailed homeless guy. 

I also love clues that are not closers but are pivotal, like the discovery of the Criss Cross scheme in The Double Down and the heart shaped glass in the cake on Food To Die For. These are both great ideas but also fun to see them being acted out, particularly the last one. 

But as far as endings are concerned, I like it when the ending turns out to be very mundane. Like in the season closer. There were more of those during the first season, I think. 

And what I would like to see: Beckett closing a case the same way Castle does, by putting two and two together that someone else said, in this case, naturally, some theory Castle had and had been discarded, and having Beckett pick it up again in the face of new evidence. The more outlandish the better. That would show a different angle on the 'communion of minds' that the characters share. What do you say?