I will answer my own question and want to suggest the following. Post another answer if you disagree.
- Leaving a comment - anyone with at least 50 reputation can do this. If you see posts which could be improved: Leave a comment. Don't flag it.
- Downvoting - anyone with at least 125 reputation can do this. If you see posts of low quality: Vote down. Posts of score -3 and less will be grayed out and auto-deleted. Don't flag it.
- Deletion - only moderators can delete posts. Users with 4000 reputation can cast delete votes. However, please follow the guide from the help center:
When should I flag or vote to delete an answer?
You may vote to delete answers in the following cases:
- The answer is extremely low quality: There is little to no scope for improvement
- The answer doesn't attempt to answer the question; it may be a comment or a separate question altogether.
Keep in mind the site is run by you as the community. Ideally, moderators should do as little as possible.
You got the tools. Use them wisely.