Do you think it's a good thing to change or add a rule, if in the middle of a playtest you find something isn't right? Should the game be stopped, and started again with the new rules? Should we let the game end even if there is something not working?
What do you usually do in a playtest if this happens to your game?
I would agree with what's been said here. I have changed rules during playtests, but not in any grand ways. I have made minor rules tweaks that I or someone else may have suggested to make the mechanics work a little better or more smoothly.
I have also aborted a playtest where the rules were clearly in need of major work. Your playtesters' time is valuable and you don't want to waste it by revamping the whole game while they wait.
The situation also depends on the group of playtesters. Some may not be as willing to endure a rules change that will make the game more balanced to their detriment. They may be winning because of a hole in the rules that you are trying to patch. It all depends on the playtesters. I try to stick to playtesters that understand that every game is in a state of possible change and that it may affect the game as we play. You know your playtesters best. Judge for yourself what is in their best interest and also the best interests of your game.