Do I need to know about "Star Trek"...

No.

But it does help. There are jokes you probably won't get otherwise.

You don't need to be an expert but I would say, yes, you need to know Star Trek fairly well to enjoy this movie. I just saw this film today and it's kind of like the film Rain Man. But in PSB, a woman plays the lead role, and she's really into ST kind of like Raymond was really into The People's Court.

I thought it was a good movie but not as good as RM. I'll give it a 7.0 out of 10. For the most part, it's basically an odd take on an adventure film mixed in with comedy/drama. It's solid entertainment in my book.