Today's puzzle is a good example of why people can find the puzzles annoying.
http://en.lichess.org/training/20301After finding the main moves, you are left with a position that Black has Q and 2 pawns for a rook, and then suddenly you have calculate every possibility to determine how to mate quickest. Thankfully(?) it gave me the "good move you can do better" on my first two tries.
Agreed. I understand that the puzzles are supposed to train "perfect" play, being play which requires the fewest amount of moves to force a mate, but this one was particularly ridiculous. I got three "good move"s myself before finding the solution.
the puzzles are generated automatically.
Also, that is a fairly easy and straightforward mate.
In the high level of puzzles, you have to continue the game with 2-3 perfect (!) moves after you won a piece or did smth instead.
This is very hard, because you'll fail the puzzle even with inaccuracy
No, it's completely appropriate. High level puzzles are for people who are good at tactics. If you are good at tactics, you should be able to calculate a mate in 3. That's not hard.
and how about this one ?
http://en.lichess.org/training/14488we can mate in 2, but engine says 'its best mate in 3'
there is a lot of problem like that one...
Yes, that one is broken. It's also rated negative so it should be removed soon.
Yeah, since the puzzles are just user games, it's entirely possible to game them by playing yourself, though I don't really understand how it is decided which games will be made into puzzles (and I'm too lazy to code dive).