@OP: Yes, we can give feedback.
First, we can add a comment after we've attempted a problem. After either passing or failing a problem, scroll down to see people's comments, if any. Below them, you should see a link that will allow you to add your own comment.
Also, we can suggest tags regarding which specific tactic(s) are featured in a particular problem. Usually, tags have already been suggested by members previously. Once they have, we can agree or disagree with them by clicking the thumbs-up or thumbs-down icon (because sometimes members are mistaken in the tags chosen).
Finally, please be advised that Tactics Trainer problems are very rarely wrong. In the comments section, people often point out what they think are flaws or mistakes in a problem, only to have another member point out why their "refutation" doesn't work at all. If you are absolutely certain that you have found a faulty problem, you might also click the "Report Problem" flag in the upper-right corner.
What specific problem ID number had this flaw?
What are the thumb up and down for on the tactics trainer?
Is this a way we can give feed back regarding our opinion of an exercise?
I ran into a problem twice. While being asked to pick the correct moves, I found myself declared wrong, even though the final move I chose was still checkmate. It isn't my fault if there is more than one way to win in the same amount of moves. If this isn't a way to report such a problem, is there a way we can still match the moves in masters' games, but have each move reviewed more objectively, instead of us having to pick the exact move they chose, though our may be just as adequate or perhaps even better?