Another trivial case--the position shouldn't have more than seven pawns on either the a or h files.
Impossible Checkmate?

@pompom: I guess if you add a white rook to the a file then it will work?
But that's basically the same thing as the four queens from before. (You only need two of the queens, I think, btw.) Maybe this is the best kind of example after all.
@einstein: Is it because of the missing black rook? (How could it have gotten out from behind the black pawn line?)

What I'm going to ponder now is the question whether there are positions like this where it takes at least two "reverse moves" to be forced into to a manifestly illegal position. Or proof that there can't be any such checkmate position.
What "manifestly illegal" means as opposed to just "illegal" will be something I'll have to figure out. It may turn out there's no useful such distinction...

@pompom: I guess if you add a white rook to the a file then it will work?
But that's basically the same thing as the four queens from before. (You only need two of the queens, I think, btw.) Maybe this is the best kind of example after all.
@einstein: Is it because of the missing black rook? (How could it have gotten out from behind the black pawn line?)
That is part of the reason. TheMouse has the correct explanation in post #12. You can say that the rook can't get out. That is true. But white can still get in there and capture it with a piece. The main issue is white's pawn structure.

What I'm going to ponder now is the question whether there are positions like this where it takes at least two "reverse moves" to be forced into to a manifestly illegal position. Or proof that there can't be any such checkmate position.
What "manifestly illegal" means as opposed to just "illegal" will be something I'll have to figure out. It may turn out there's no useful such distinction...
You might be interested in a thread like this. It talks about both legal and illegal positions. It is mostly positions that are not checkmate though.

Here is one that has checkmate. There has been some work done in that forum to determine if the position is legal or not.
Is there a such thing as a position which constitutes a checkmate for one side, but which can't be reached by any legal set of moves.
Let's leave out positions with white pawns on the first row or black pawns on the eighth. ;)
Hrm and let's also leave out positions with more than eight promoted pieces on a side. :D