You have a few options
The stack has two main methods for communicating suggestions for improvement; commenting and editing. When and how to use these tools is a skill that improves with practice but I'll try to give you a quick overview. You also have the option of posting your own answer.
Comments are the main method for providing feedback on a post (other than voting). It is worth reading the comment everywhere privilege information for official guidance on what they are and how to use them. Also check out my answer on How to write a stack exchange comment? for some general advice.
I'll give some specific examples of comments you can use for the situation in your question.
When an answer is mostly good but mis-quotes a rule or misses a key fact, you can comment something like:
Most of this answer is good, but you might have overlooked X...
- Then go on to explain more details if required. If possible link to a source to support your point.
When an answer is correct but the structure is making their main point difficult to find:
You might want to highlight your point about Y. I think it's great and important to the answer but is currently being lost.
- You can also suggest re-ordering their answer or adding a clearer title.
When you know an answer is correct but it is lacking support:
I believe this answer is correct, but it could benefit from adding additional support. Can you edit in some rules or citations to support Z?
- If you know the source they need you might like to link to it (or edit it in yourself).
A similar case is when the answer might be correct but you can't tell because it is lacking support:
Can you please provide some support for this answer? Why does X work that way? Editing in some rules or other citation would be beneficial.
- You can also flag these posts for moderators to add the "citation needed" banner if it is particularly problematic.
If the answer has lots of problems but makes some good points and you feel like you could fix it but don't feel comfortable making that large an edit, you can ask for permission:
I think this is a good answer that could be improved with a few changes. Do you mind if a make a major edit to focus this on your best points?
- Alternatively you could make the edit and then ask them to rollback if they disagree.
- This is often best if you are dealing with a new user and think it may be difficult to communicate exactly what is wrong with the post in a way they will understand.
- I usually use this after one or two other comments have failed to get the point across.
When an answer has an incorrect assumption that leads to an incorrect conclusion.
Answer says "X, Y, Z therefore A" but Y is incorrect. Leave a comment like:
I think you've got Y wrong (here's the link to why) which makes the answer B, not A. Please take a look again.
The upvotes on your comment will likely indicate if you are correct. If you see a comment with more votes than the answer it is on, that's often a sign that something is/was missing from the answer.
If the OP edits their post to address your concerns, or if they make a logical argument as a refusal to do so, it can be a good idea to then remove your comments if they are no longer relevant. This helps clean up the site and make it easier for everyone.
The editing of posts is a key part of our model. Anyone is capable of suggesting edits to posts. However you don't want to completely re-write someone's post, particularly if you are correcting something you believe is wrong.
Editing for formatting and grammar:
- You are always encouraged to edit for formatting and grammar.
- We encourage the use of proper headers
# over bold for accessibility reasons.
- Fix spelling and typos, except for regional spelling differences (don't change s to z if used consistently in a post).
- Edit game terms to match style from source books. Using consistent style makes it easier for people familar with the system to understand. For example check out V2Blast's excellent 5e style guide.
Editing for logical consistency:
- If you believe you can improve a post editing is encouraged.
- Try to preserve the original intent, don't completely change their point to be correct.
- Edit the whole post, don't fix one part and leave errors or typos in another.
- Make it a cohesive post, don't signal edits.
- Leave a comment explaining why you made your changes and asking them to rollback if they disagree. Alternatively use Nitsua60's excellent suggestion:
Go ahead and make the (possibly quite large) edit that you think makes the most easily-followed version of the argument being presented. Then immediately roll back your own edit and leave a comment saying "I think your answer's good but hard to follow. I went ahead and gave it a rewrite which you can find as version N-1. If you think that is better go ahead and roll back to that version, and I'm glad to have helped you make your answer better.
Write your own answer
If situations where answers make good points you think are important but are otherwise poor answers, it might be worth extracting those points into your own answer. When adding an answer to the question keep a few things in mind:
- Write a complete answer, you need to address the entire question an be a complete answer without requiring readers to read the other answer.
- Give credit if you feel it is due but don't feel like you have to.
- If you think someone made a great point and should get credit for it, include a link to their post in your answer.
- This isn't a rule and you are free not to do it, but some people do consider it polite.
- Add something new.
- If you are simply restating what is already there then you need to make sure it is a significantly better presented answer.
- If you can, add some additional information or context as well as improved structure.