When is it rude to say to someone that a taken cube was a drop and later say of checker play that "that was a mistake"? Or perhaps it would be easier to say when it's not rude?

IMO, it depends on some factors:

1- Whether the commentator is playing or watching. If s/he is one of the players, his/her opponent might feel hurt and might think that this is a way to confuse/ridicule him/her.

2- Whether the commentator is an experienced and skilled player or not. For instance, I would LOVE to get comments on my moves from a well-established expert like dorbel, zyxtcba, Zorba, etc. But when a sub 1500 rating guy tells me I'm wrong, I may get upset.

3- Whether the commentator is a friend or not. I would never feel bad if a friend, even yeti, comments on my moves.

4- Whether the match is an important one or not. For instance, if the match is for money or in the final round of a tourney, kibitzing might be considered as an immoral act and actually in Escoffery tourney, it's completely illegal.

Regards

Thanks for the comments. Yes, I think it depends, too.

lewscannon got this particular instance correct. I'd show you the conversation log if my 3DFibs hadn't crashed during the match. I only got the aftermath. It was a complete stranger, rated 70 or so below me, who turned out to be an arrogant douche ( not a term I use but it's a good one!). In our second game (immediately after the first in which practically no conversation unrelated to line connection problems occurred), he told me that a cube that I'd taken was a drop. I asked him whether he was telling me that I made a mistake. His flippant reply was "You said it". Later he said "That was a mistake" out of the blue. In neither instance did he offer more than that bluntness. I assumed that it was more gamesmanship and challenged him again: "Are you trying to be rude?". The conversation didn't get friendlier. Apparently "we", that is "all Fibs players", are okay with his sort of behavior, even those who are complete strangers to him.

I gave him a lecture which he didn't appreciate, though maybe a couple of points sank in over the next night.

Yeah, and maybe there's no sugar in Homer's doughnuts.

We shan't be resuming the game that he preferred to drop rather than continue after a pause to discuss his attitude. Nor shall I be able to respond to his parting "dickhead" tell followed by ignore, which informs me that he's really a very sweet chap underneath it all and by no means a coward.

Btw, would someone kindly send the link for this thread to uzalla the douche. 

It depends on the circumstances and, vitally, upon how well you know the opponent. If you're playing some dickwad that wants to annoy you (and you're sure they're not a dropper - unlikely I admit) why not have some fun with them? Pretending to be stupid (eg asking "how should I play that?" after an opening 3,1, "was that a good roll?" after a 35:1 shot, "is this a double?" anytime after their Crawford match) often works well.