Most important is that you’re not a lower belt rank than the one you’re criticizing, otherwise they might “put you in place” next time you roll.

That's an excellent question, because how do we get better as instructors without feedback?
The other side of that is that many people do not actually want feedback and to even offer it can make them defensive or angry.

I'm a teacher as my career and I work with mentoring other teachers / student teachers.

In my experience you need to be as non confrontational as possible.
Give feedback in a private setting where people won't feel embarrassed.
Frame your feedback as support to help them achieve their goals, not as criticism.

For example, to help children be more open to assistance I start by acknowledging their success and offer help / suggestions to help them achieve even more success.

It also works well with adults.

So you could start by thanking the instructor for their time, point out something you enjoyed about the session and then ask about the areas that were not as effective for you.
"I was hoping we'd cover more of this concept..."
"I found this bit difficult to grasp, could you maybe show me in a different way..."

It's sad that this is almost definitely true.... I like Benny's approach but you'd have to be unwilling to recieve feedback for it to be really necessary, although it is a 'nice' way to package the 'constructive criticism'. There is a big difference between giving feedback and helpful tips and just being rude.

When training at other schools I always wait to be asked for my input or ideas even if I think there is a better option or way of teaching it.
I have had it happen on multiple occasions where I'm teaching and people just butt in. Where I once taught one guy (who was irregular to my sessions) would always butt in and say, 'that's good but do you mind if I just teach it better'... WTF!

I'm constantly asking for feedback because I want to improve but that's the thing... I ask for it, I can't be upset if I get bad feedback (unless it's bullshit) even if it's from a lower rank.
(I have recieved a lot of bullshit feedback that wasn't accurate and given in spite).

It all comes down to the shit we learn at playschool:
*Treat others as you wish to be treated
*Play nicely
*Share your toys (lower ranked training partners)
*Respect the teacher
*Try not to be a c#*!t

In my experience, very few people are willing to receive feedback on what they do, unless the person giving feedback is their boss or a respected mentor

Having been on both sides of this fence, I have felt being put on the defensive when (then a purple belt) challenged a technique that I was teaching (in a group class of mixed levels) of a "better" way of a technique, not taking into account there were beginners to brown belts in the class and in a way, speaking up for the purpose (I felt) to show how clever and knowledgeable he was and that he had a better solution.

No one likes a Smart Alec in such situations, and I would have preferred that the individual asked me during the partnered drill part of the class, how his approach would be more applicable for him at his level and abilities separately from the main group explanation as doing so, while beneficial for the advanced students, quickly leave the beginners glossy eyed and quickly losing interest. Then again, this individual has always had this type of personality (somewhat insecure and wanting to stand out from the rest of the group by being vocal irregardless of making comments whether he was in the right or wrong but just wanting attention), so it was a valuable lesson nonetheless.

I always try to get feedback from the beginners if I'm showing a technique at that level and believe that if they can "get it" then I'm on the right path, however over the years I have learned to simplify the movements to coach to the lowest / slowest learner and ramp it up in complexity and details for the advanced students. I try not to use a fixed method of teaching but getting feedback, observing how the students perform in isolation and under pressure is a few of the ways for self-critique on my coaching skills. Attending workshops is learning how other coaches present the information as the main point of interest and the techniques a close second.

You need to have a good relationship with the person you're giving feedback to.

If you don't know them that well then you can just check if they're actually ready to listen.

And then give you're feedback like any good feedback is given - speak from your perspective using I-centric message (Thomas Gordon), possibly point out something that was good and how and why things would be improved...

You can't criticize without offending. You can however ask questions after the instructor has taught the technique to the class, i.e. when you're drilling the technique. Note that I say ask questions vs critique. You have to figure out a way to ask the right question relevant to what you see missing or wrong in the technique taught. Anyway, that's been my approach and even this fails sometimes and for sure there's been times where I offended the instructor. Sometimes you dislike the entire format of the class vs just how a technique has been taught ... only way to address that is if you are good friends with the instructor and even that's tricky.

Good question by the way.

Constructive criticism, honest questioning, never attack the character/person.

If I see a higher rank teaching something that I suspect I could teach better, I ask questions to lead him to that. If they don't find their way there, I just shut up. It's not my class after all and I might be wrong and maybe they do know better. Either way it's not a problem.