I don't have high rep on this site, but I do on Stack Overflow, and here's what I expect:
I usually can't tell the rep of people who comment on my answers. I could tell if I went and looked at their user page, but usually I can't be bothered, and so usually I can't tell.
So, I usually respond to the comments of low-rep users exactly the same way that I respond to the comments of high-rep users I don't personally recognise from previous questions. I can't do otherwise.
In the context of StackExchange I feel that a comment that's just a factual statement of my inaccuracy is perfectly polite, regardless of the rep of the person who makes it.
Provided it's a matter of correctness and not opinion, there's no real need for prevaricating language like "I may be wrong, but", "I think I've misunderstood", or whatever. If you feel like it makes you less of an ass when you're wrong, OK, have at it, so long as you make it clear exactly where the point of disagreement lies. Don't make a vague objection for the sake of politeness, leaving the questioner to figure out why you're right or wrong, maybe argue with you at cross purposes for a while.
Phrasing the correction as a question is probably the cheapest way to "back off" a bit from your claim, without wasting your time and risking confusion. "Do those two lines really meet? What if they're parallel?". This also has the advantage that if you're obviously right it looks like a humorous rhetorical question, whereas if you're wrong it can quickly be answered straight: "yes, in this geometry any two straight lines intersect, although their intersection might be the point called "infinity". See X for more information."
You might want to put a bit more work into convincing yourself that you're definitely right, the higher your regard for the person you're questioning. But that's purely a balance of probability thing. What are the odds that a mathematical genius wouldn't know what Cauchy's Theorem is? Pretty small, so if you think they've called some completely unrelated thing "Cauchy's Theorem" then you should reflect on whether maybe there's more than one. Same goes for matters of terminology, they might simply have made a different choice from what you're used to. What are the odds that a mathematical genius would make a simple arithmetic mistake in an answer on this site? Reasonably good, and quite aside from their mental arithmetic they don't necessarily type any better than anyone else and so errors can get in that way too. But once you're convinced you're right, get on with it.
If it is a matter of opinion not accuracy, that is to say the answer is true but perhaps not the most helpful way to approach the question, then just downvote and comment if you feel like it. You're probably somewhat more likely to wind people up this way, though, unless they've thoroughly misunderstood the question and can be easily put straight.
Anyway:
- Superhumans make mistakes.
- There is almost nothing worse for a superhuman than reaching the point where nobody corrects them any more even when they're wrong. Quality goes through the floor.
- Nobody is entitled on StackExchange to the deference that, for the sake of not wasting time in class on your errors, you might give to an academic superior or an instructor. There is no "after class" or "in a private email", just question them now. Of course that applies in some classes too: I don't mean to say that all instructors should be deferred to.
- Even if you're wrong, superhumans are on the site because they want to help out us mere mortals, so they quite likely won't mind at all dealing with your incorrect objection by teaching you the rights of it.
- Even if they do object and choose to make you look an ass, well, whatever, you've learned something about them. If they're right and you're wrong, admit it and move on.
- You will remember your humiliations far more clearly than anyone else will.
