Sometimes a comment is valid, but then the user makes the requested correction leading to the comment becoming obsolete. If I flag the comment as obsolete, will that harm the user in any way?
No, why would it?
The obsolete comment will disappear (if other users flag it or a moderator agrees with your flag), and that's about it. The only comment flag that may "hurt" the user is the "rude or offensive" one, depending on the circumstances it might lead to a suspension. But "obsolete" is absolutely harmless.
No, it will not. Users with many deleted comments are still allowed to comment, ask questions, or answer.
If you flagged the comment as obsolete, and the moderator who handled the flag noticed it was another offensive comment from that user, that would be different.