The audience laughed in San Jose opening night (I always maintain it is his expression that generates the laugh, not the 'war cry'.)
When I saw it two nights later, there were a bunch of people who were laughing uncontrollably during Spock's funeral. That's the only time I saw that happen, though I can understand thinking the bagpipes an odd choice (these people were laughing BEFORE the bagpipes, though. I was not among them.)
We all laughed when Kirk falls on his ass in SFS on opening day. I still think that is as failed a moment as any in a TOS flick, that they completely mis-staged it.
I think the biggest accidental laughs in TOSflicks are Shatner's '0h migod' in TMP's transporter fritz-out and "ohmigawwd' in TWOK (when they find Chekov in the hamper-fridge.)
I don't recall anyone laughing at the Khaaaan!!!! scene. But I believe I saw the first showing along with my usual geek posse. Science fiction is serious stuff! You wait overnight to get the best spots in line.
I did chuckle when Spock was dying. For some reason him straightening his jacket and walking into the wall is funny to me.