First I'd like to quote from the Help Center page on editing posts:
Editing is important for keeping questions and answers clear, relevant, and up-to-date. If you are not comfortable with the idea of your contributions being collaboratively edited by other trusted users, this may not be the site for you.
When should I edit posts?
Any time you see a post that needs improvement and are inclined to suggest an edit, you are welcome to do so. The original author of a question or answer may always edit their own post, regardless of reputation level.
Edits are expected to be substantial and to leave the post better than you found it. Common reasons for edits include:
- To fix grammar and spelling mistakes
- To clarify the meaning of the post (without changing that meaning)
- To include additional information only found in comments, so all of the information relevant to the post is contained in one place
- To correct minor mistakes or add updates as the post ages
- To add related resources or hyperlinks
My own philosophy towards editing is that you should endeavor to make edits that clearly help the original post, and will not annoy the original poster. It's important to preserve the meaning of the posted question as faithfully as you can, but it's fine to clean up the wording of a badly worded question. There are really two conflicting goals here:
Don't annoy other people.
Any edit that clearly satisfies both goals ought to be fine.
In the example you link to, I thought the proposed edits ranged from clear-cut (e.g. "their" to "they're", "student" to "students", and "cheg" to "Chegg") to marginal, but overall I think I would approve the edit.
In general, I think the following types of edits are usually fine:
Fixing capitalization, punctuation, and spelling.
Adding paragraph breaks to long posts that don't have any.
Adding LaTeX to posts that include non-LaTeX equations, and fixing LaTeX mistakes
For a post written by a non-native English speaker, changing word choices to those that a native English speaker would make, as long as the meaning is preserved.
For a very poorly written post, changing it in such a way that it meets the minimum quality standards for a question, while roughly preserving the meaning.
For a very unclear question, adding material from the comments that seems necessary to clarify the intent (assuming the original poster does not add such material themselves).
Improving the title of a question so that it better represents the body text. For example, if you find a question with a vague title like "Problem Students", I think it's fine to change it to something that better describes the body text, e.g. "How to handle students who monopolize class time with questions?"
Improving the tags of a question.
For major edits (such as those near the end of the list), I think it's also polite to leave a comment mentioning that you have made the edit. I see a lot of users doing this with tags, and I hope that someone would also do this if they changed the title, or made major changes to the text of a question.
Finally, if you make an edit and the author of the question (or another user) reverts it, please don't get into an edit war. Just move on to another question!