I found an incorrect puzzle--- how often does this happen?

edit: formatting, adding a link to the puzzle

In your starting position (which Black wins with the move), it only takes Stockfish 13 a few seconds to find that 43. Kd3 draws for White. In the line you give, 44...h4 is Black's only move to avoid losing, but then 45. e5+ is White's only move to draw, which Stockfish sees at a depth of 20 after 7 seconds.

It's hard to believe that Black was supposed to win this position with White to move. I couldn't locate the puzzle on this site. Is there a way to find a puzzle by its number?

The white move was probably given as the "puzzle introducing move" which is often a bad move. Black then was supposed to win unambiguously but clearly he can't. Looks like a case of bad "puzzle mining" as suggested by the OP.

There are many complaints about puzzle correctness but most turn out unjustified. This is a rare exception.

Btw, the first time I analyzed this position with chess.coms engine it turned out all wining scores for black. When I repeated the analysis a few minutes later it changed its mind to draws. We need not worry about the engines, they are turning human

Arisktotle, the OP gave a puzzle id number. Do you know how to find it? I couldn't figure that out.

I used to know but I forgot when I found most are inaccessible to me. I suppose it depends on membership or it changed over time. There is a team continually tuning and tweaking chess.com functionality - some for the good, some for the bad, some intentionally, some accidently. There is no accessible maintenance log so there is no way to find out whether there was an error or a change in specification. It's very frustrating. 

That's interesting. I recently posted a White to play and draw position in which White had to take the long distant opposition instead of the distant opposition to draw. The chess.com engine called the one drawing move an inaccuracy, and gave a losing move as White's best. But I have a basic (free) membership, so I can't run the analysis at full strength. Stockfish 13 had no trouble with the position.

Oh, here is how to get to the puzzles (example): https://www.chess.com/puzzles/problem/681992 

Thanks. I looked up that puzzle, and at the top it says Black to Move. With the move, Black wins with Nxd4+. But the OP mentioned moves given in the solution, and I don't know how to bring up the solution.

Yep, this happens because we break into the puzzle using the url. When you go there decently through the puzzle interface, then the interface first plays a (stupid) white move from the diagram before it has you solve the problem as black!

"Skipping the puzzle interface" is also the reason why you cannot bring up the solution or solve the puzzle through the url. You need to get there though one of the puzzle modules (I use puzzle rush) but these will not allow you to pick your preferred puzzle number. Chess.com intentionally gives limited access to the puzzles. How many and which you can solve in a day depends on your membership type and puzzle rating.

You can see the solution by clicking the arrows in the bottom right of the puzzle page https://www.chess.com/puzzles/problem/1216370. At least, I can; hopefully that feature is not member-restricted. 

When you encounter this puzzle in training, it shows white to move, white plays 1. nc5, and then you are supposed to find the refutation, when in fact there is none. 

edit: I just saw Arisktotle covered most of this  already. Woops! My bad.

I agree, I'll often check the comments of a totally fine puzzle only to see someone complaining that the puzzle is wrong. Here, I found no comments, and the puzzle was in fact wrong!

I reported it, but I'm worried my report won't get noticed with all the incorrect reporting that probably goes on. Do you know a way to draw further attention to this puzzle? I'd love for the problem to be fixed.

I see  <  >  at the bottom right under the green box, but they are grayed out and don't respond to clicks.

Oh dang, that sounds like your access is restricted. I can also play through it by pressing the corresponding arrow keys, but if the arrows are greyed out for you, I doubt that will work.

The puzzle "solution" is the same line in my original post, though, so you can see it there. Like I said, white plays 43. nc5, and then you are given control, and supposed to play 43...Bxc5, even though that draws.

I see. Before the knight moves, Stockfish finds five drawing moves for White. If they wanted a move that would give Black a win, Ba7 would have been a good choice.

Haha, you're right! Hard to imagine a human playing Ba7, but that would make a better puzzle than this one!

It might have made the puzzle too easy, but Black might have been tricked into letting White give up the bishop and e-pawn for the black pawn, which would have drawn.

Yeah, after say 43. Ba7 h4 44. Kd3 h3 45. Bb8 Black has to play 45...ne5+ to win, which might trip someone up in puzzle rush for example.

I was thinking about 43. Ba7 h4 44. e4+ Kxe4 45. Bf2 h3 46. Bg3 h2? 47. Bxh2 Nxh2.

Interesting indeed.

That makes sense, the only thing I'm questioning is if Black has multiple winning moves at some point in that line. Stockfish (chess.com's version, depth 28) says on move 46 that Black can win with 46...nd4+ or 46...Be7, although we've already seen the engine can't per se be trusted in this ending. I chose 43. Ba7 h4 44. Kd3 h3 45. Bb8 ne5+ for my puzzle because according to the engine all of Black's choices are only moves. But again, who says we can trust the engine? Designing puzzles is pretty hard!