I always correct in my own native language (because english for example, is not a language I "master") and only when I feel I can contribute to enrich the text. I replace the words that are wrong or that doesn't make sense, and I add new words/new proposal.
If you say that we shouldn't correct when there are already one correction, I say no. Because sometimes the corrections are wrong, or they miss some mistakes. And I don't want to argue to say mine or his correction is better than other ones.
I feel happy to correct because the prodigious shows goes on and that I may contribute a verse (Dead Poet Society)