The downvote tooltip covers when to downvote:
Questions: This question does not show any research effort; it is unclear or not useful.
Answers: This answer is not useful.
In particular, it's based on usefulness, not correctness nor agreement. This means we might downvote useless posts that we agree with, and upvote useful posts we disagree with.
Over at Islam.SE this distinction was a big problem: users from one sect would e.g. downvote well-researched answers from another sect based on disagreement. It became a popularity contest.
In essence, a popularity contest serves nobody very well. Votes should reflect the usefulness, relevance, and self-consistency of posts. That might mean downvoting correct answers.
Jon Ericson, Please vote based on quality, Islam.SE Meta (see also Disagreement should not be a basis for down-voting)
This prompted the notion that we need to Back It Up, which basically means provide evidence to support claims in answers. (And it's important to note that we are all random people on the Internet.) It stemmed from the blog post Good Subjective, Bad Subjective.
So when upvoting answers, we should keep an eye out for:
- useful: pinpointing the underlying general problem, the relevant grammar patterns, etc.
- useful: reliable references, e.g., textbooks and dictionaries, links to reliable websites (ideally quoted to alleviate link rot), videos by Chinese teachers, etc.
- useful: example usage beyond the original context (for verification [it's not just the author's at-the-time personal opinion], and help seeing the problem in a broader context), etc. [noting the OP is maybe 1% of the readership]
(And probably a bunch of other things I haven't thought of.)
And when downvoting answers...
- not useful: it's fundamentally incorrect, or doesn't really address the question.
- not useful: skeletal posts, e.g. "XYZ is correct" or "it means ABC", where the explanation is missing. This is where we might downvote a "correct" post we "agree" with---it's incomplete.
- mostly not useful: appeals to authority, e.g. "I'm Chinese and I say XYZ is [in]correct". Native speakers can be wrong, and often have strongly held language biases.
(And again, probably a bunch of other things I haven't thought of.)
Compare this to someone asking for help with their maths homework, and your response is "I'm a mathematician; answer C is correct". What have they learned? (This answer would probably get downvoted to oblivion at math.SE [even if people agree it is correct].)
As for commenting, I try to limit myself to at most one comment per post, and strive to pinpoint the precise problem. It's okay if the author doesn't agree (and replies such); I've said what I needed to say, and the future reader can decide for themselves. (And maybe I'm the one who is wrong!)
I think that's a reasonable way to highlight issues without long threads (which will probably be ignored anyway).