A double check where both checks create a mate?
What's the rarest kind of checkmate?

I've had a promotion to knight checkmate once, ever. It was a game with the guy who taught me to play. He had a massive material advantage, was busy mopping up my few remaining pieces, and didn't much care that I was marching a pawn towards his back rank, because his king was so securely walled up by his own pieces that there was really very little damage a queen could do.
"Checkmate."
"Don't be ridiculous, how could that possibly be checkmate?"
"That is not a queen, that is a knight, and that is checkmate."
I have savoured the look on his face for thirty years.
[Removed - DB]

I assume that your checkmate didn't lead to his complete mental breakdown and subsequent criminal activities, although it is very unclear from your post...
Since the two events were several years apart, I think that's a safe assumption. We'd parted ways after he stole from me and blackmailed my mother, among other things. I then told everybody we knew that he was a very dangerous scumbag, and nobody believed me...
He was a good chess player, though, even before the life sentence, which probably made him better still.

I think that castling is the rarest checkmate, because it is usually done early in the game, before any serious attacks ca be made, with the exception of brand new players.
Is it castling, en passant, king discovered check, or something else?