@OP: Chess Mentor, Tactics Trainer, and the Daily Puzzle generally want the fastest checkmate. A move that comes closer to mate or achieves a forced mate may not be good enough if a faster mate can be found.
Can you give an example of a Chess Mentor problem with multiple solutions? If it does have multiple solutions, it may indeed be a flawed problem, and the staff would appreciate being made aware of it.
Most of them have another nuance involved. The trainee will miss a tactic and ask, "why did I have to capture with the rook instead of the queen? why can't I just capture with the queen...it's the same thing."
Only, it's not the same, because the one you chose that signaled your answer incorrect provided a flight square for the opponent's king and the correct answer resulted in checkmate.
I get what you're saying, Learning; that's why I was contrasting what I ran into with finding the "best" move--there really is only one best.
As a recent example, "Essence" EXC010 wants you to find mate. Easy enough--Qd8 mates. However, the game tells you that's an alternative move; unless you use the equally mating Qf7, you don't move on and, as far as I can tell, lose points. While I understand the CM points are basically meaningless, it adds another level of frustration. Where other problems have nuances and will alter play deeper into the game, mate-in-one is mate-in-one, so why does *which* mate you choose matter?
It would be a little like handing someone a totally empty chessboard and a knight and asking them to place it where it can cover the most squares. They choose d5 and you tell them that that's an alternative move, but the correct one was f3 when they're both perfectly valid placements.
@OP: I have very little experience with Chess Mentor, having completed only about 20 lessons, but my understanding is that one is not penalized for finding alternate correct moves--though the lesson will require you to find the other move(s) before progressing.
I really think that the program doesn't truly care about which mate is found, in terms of rating points. If your solution were actually inferior, even if only slightly, you would probably have received an "Incorrect" assessment with an accompanying explanation saying something like, "Your suggested move is really great, but our move is even better." But the "Alternate Correct Move!" note is supposed to mean that the move played is just as good as the "Correct!" move.
If it's actually rejecting a mate in 1 move, then that's a design flaw. Just try to ignore that flaw and keep learning the patterns / ideas it's trying to get across. As you said it's not like you can cash in the points for money or something :p you're there to learn about chess.
I know mate in 1 is super simple, and I'm sure you're right, but in anything more complex than a mate in 1, be sure your solution actually works. It's usually instructive to take a failed tactical solution and find out why it fails. Sometimes beginners have a tendency to think "my move works too" and ignore the given solution. Don't do this.
I guess with tactics on computers now it's not as much of an issue. I started tactics in books. In all the puzzles I've ever done I've only ran into 1 "incorrect" solution, and it was in a book. Well, it wasn't incorrect but you pretty much captured a pawn and so did they... there was no tactic lol.
You don't lose points for an 'Alternate Correct Move'. You just don't advance until you get the one they were looking for.
Oh, CM is chess mentor. I was thinking of the lessons that come with the chess master program.
I don't worry about those types of positions, after all, if you were in a game situation you chalk up the point whichever move you make. The really 'Psychic' Mentor lessons are the ones for openings where you don't know which variation of an opening they want you to play and its just guess work for at least two or 3 moves. For example its ridiculous to take points off somebody who doesn't know that the author wants them to play 7..Nbd7 rather than 7...Nc6 at that point in the Kings Indian when both of them are viable moves for the knight.
I gotcha, Waffle and no problem on the confusion. I go back over ones I've messed up and recheck my move ("Oops! Yeah, that Bishop is going to eat me alive if I do that.") and again after enough time has passed that i likely won't remember the particular puzzle to see if I can figure it out this time. Same with book problems, although I do like to lay them out on a board--3 dimensional just seems to "click" better than a 2 dimensional page/screen layout.
Ugh, Vease; you are not making me look forward to opening theory. 
All in all, it really is improving my seeing of the board. I just needed to vent, I guess. Back to learning...
I've really been enjoying CM except for one thing: it asks me to find mate and I do, but it wasn't the mate the creator was looking for, so I'm required to keep looking for the one move they want. It doesn't matter that what I did was also right and gains the checkmate, I still need to find which particular checkmate he wants. The same thing happens when you're looking for a move--there may be 4 or more alternative moves, all good, all legal, but you wind up playing through seemingly endless iterations of, "That's a great move, but find the particular one I had in mind." Arrgh.
I'm not talking of where you're asked to find the best move--there can be only one "best", after all. It's the ones looking for mate or "a" move; where it comes down to a stylistic choice as opposed to a "correct" one. It's like going out to eat with someone and asking where they want to eat:
"Any where at all is fine."
"Great! I know a Thai place..."
"Oh, not Thai."
"Well, there's this bar with great burgers..."
"I'm really not in a burger mood."