I have seen several posts on tactics trainer's puzzles in which people are upset with the particular problem. Though I agree that the problems themselves can be frustrating, it is important to understand the goal of tactical problems to find the correct move. The point of tactics trainer is to find the best move in any position. It does not always result in an immediate win, and sometimes means achieving a draw. The goal is making the best move in the position given. The best move can mean any of the following:
1.) Checkmating the opponent
2.) Creating a material advantage
3.) Drawing an otherwise lost position
4.) Winning an otherwise drawn position
5.) Solidifying a dangerous position while maintaining a material advantage
(I may have missed a category, but that covers most of them)
This being said, you must make the best move in the least possible number of moves.
A couple of side notes: I have never seen a tactic result in a loss, which makes sense. Also, there must be only one "correct" move in each step in the sequence for the tactic to be valid. This means the tactic should end if there are two possible ways to continue for checkmate in an equal number of moves. This knowledge is advantageous to the puzzler because if you see two paths to checkmate in 3 moves and both require a different first move, then there must be a checkmate in 2 or 1 or the puzzle is bad because of ambiguity. Having an opponent make a bad move during the solution is not grounds for removal of the puzzle. All that is required in a puzzle is that the puzzler makes the "best" move in each position that is given. I do not agree with the fewest number of moves entirely because it does come up sometimes that several moves are winning, but only one would be correct in a tactic puzzle. That, however, is a completely different topic.
Finally, here are a few things to keep in mind when trying to do well on tactics trainer...
1.) First look at which color you are playing as
It can be really annoying to find out after some time you are actually black and not white
2.) Look at the coordinates on the board to see which way the pawns are going
White pawns move towards the 8th rank, black pawns move towards the 1st
3.) If the timer is going down really quickly, the solution is probably only 1 or 2 moves
That speaks for itself
That's about all I can think of. I know tactics trainer isn't perfect, but I hope people will look to improve themselves before raging at how terrible it is.