Quote Originally Posted by Raistlin View Post
If you're ever writing something where grammar is an issue, you shouldn't be using contractions in the first place.

That said, grammatically, "could've" and "should've" are fine as far as I know. MSWord does not consider them a misspelling.
Yes they are correct. Contractions of "could/should have." The error would be saying "could/should of" or "coulda/shoulda."