Is it okay to correct someone's grammar during a conversation?

It depends on context and your relationship with them. If it's a close friend or student and you're genuinely trying to help, sure, but do it gently and privately if possible - nothing kills a conversation faster than feeling like you're being schooled in public. I've been guilty of this myself, especially after a few drinks at faculty gatherings, and let me tell you, it's usually not worth it. Save the corrections for situations where it actually matters, like if someone's about to give a presentation or something, otherwise just let people talk and enjoy the moment - that's my philosophy anyway.