We don't have any policy that I know of - it's up to the discretion of individuals to approve/reject/vote as they see fit.
Just to be clear, approving/rejecting edits is not solely a moderator function. Anybody with the edit questions and answers privilege (i.e. anybody with at least 2000 reputation) can vote to approve/reject an edit, and I think it only takes 2 or maybe 3 such votes to either finalize or drop the edit.
Consensus on MSO (our "mother meta") is that signatures and taglines should be removed; in fact, the FAQ even says not to use them:
Can I use a signature or tagline?
Please don’t use signatures or taglines in your posts. Every post you make is already “signed” with your standard user card, which links directly back to your user page.
So people shouldn't be rejecting edits that remove signatures/greetings.
On the other hand, I probably would reject an edit that only contains minor formatting changes or the correction of an "i" to an "I". I don't like poor punctuation either, but those types of edits really don't add anything substantial, and they bump questions/answers that really, in a big-picture sense, haven't actually had any new activity.
That's just my personal take on it and once again, there isn't a formal policy or set of official rules for accepting/rejecting edits. But, in my personal view, removing signatures = OK, changing lowercase letters to uppercase = not OK.