In my 20 plus years at the gym, I have seen many crazy stupid things. The worst was one case where a trainer worked a guys so hard he fainted. We thought he had a heart attack, but an EMT came and carried him out. I knew when I saw him sweating profusely and turning pale that he was going to fall. The man was very over weight, out of shape, and older and should not have been pushed so hard. Thank God for those rubber mats. The trainer was justifiably embarrassed.
Even these day I see trainers trying to come up with all kinds of tricky exercises maybe trying to impress people that they have some secret. A simple curl or push-up doesn't seem to be enough.
Recently, I saw a trainer have someone standing on this half ab-ball thing (like an air pillow on a base) while having the beginning person curl the dumbbells that were reasonably heavy for him. I kept thinking as the person wobbled, one wrong twist or loss of balance, and that persons back is going to be very hurt.
Anyway, if the person was my friend or someone I knew pretty well, and was concerned about possible injury, I would probably say something off premises, but otherwise I would leave it alone.
I think though, PsychExerSci, that the best thing you could do to help, is get clients or friends you could train with your knowledge and education, and teach them simple safety along with exercise techniques. I think if you teach people what NOT to do, maybe other people watching will get a hint and question things, without you having to be confrontational. If you teach thing in terms of helping your own trainees, you won't look like you are trying to run someone else down and come across as more confident and knowledgeable.
Congratulations on all your education and good luck on the PhD! Its good to be an expert in something you love doing, especially if it means helping other people.