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.