Hi Michael. This is a tough one! The humanitarian part of me says “yes,” but the practical/professional/risk-adverse part of me says “definitely not,” for a host of reasons. Here are just a few reasons why in my personal opinion I don’t think that interfering with the non-client while in a professional setting (working with my own client) is a good idea (I’m listing these in no particular order of importance). First, I should be “totally” focused on my client, not others who are also working out. So, why/how did I even get to the point of noticing another person’s poor form? Second, I know absolutely nothing about this other person (for example, their physical limitations that may “require” them to use this “poor form”), so trying to “correct” something that I know very little about is a big problem (remember, there is “textbook” form for certain exercises, and then there is/are adaptations that we, and exercisers make or have to make, according to their own physical limitations and make-up, so to presume that they SHOULD perform an exercise according to the “textbook” without knowing more about this person is a big no-no in my opinion). Third, in my opinion, as a professional trainer I should not be giving “professional” advice without first having a client-trainer relationship with the other person. Do you ever see a doctor, lawyer, dentist etc. giving unsolicited professional advice to a random person that they meet or see out in public? Absolutely not! They generally will not until they enter into a professional relationship with the person. Why? Liability reasons, also because they don’t know the person’s situation (giving professional advice with limited or worse yet, NO details or specific information is a serious risk … I could go on and on about this subject, but I’m guessing that you know my opinion on this. Others may disagree, but in my opinion, it a situation with little benefit and great risk.
One caveat/exception would be if I saw someone endangering their health/life or that of someone else, but that’s not the situation that your question asks and so my answer is not intended to respond to that situation.
I hope this helps.