How we cite our quotes: All quotations are from Ghostbusters.
Quote #4
PETER: I'm gonna go for broke. I am madly in love with you.
DANA: I don't believe this. Will you please leave?
PETER: And then she threw me out of her life. She thought I was a creep, she thought I was a geek and she probably wasn't the first...
Venkman is up to his old tricks again when he hits on Dana while inspecting her apartment. Just like with the sexy young co-ed we saw him with at the top of the movie, he's using his supposed paranormal expertise to try and get a date. Dana is a lot more with it than that co-ed, though, so he's going to have to come up with a new approach.
Quote #5
PETER: I'll prove myself to you! [...] And then you'll say, "Pete Venkman's a guy who can get things done!"
The script pulls a popular narrative trick here by tying the main plot in with a love story. Peter is going to win Dana's love by taking care of her Zuul problem. It's really not a lot different than all those stories about knights killing whatever monster to either rescue the fair lady or to win her heart.
Quote #6
PETER: I'm working on that. If we could get together Thursday night, I'm thinking nine-ish, you know, we could exchange information.
DANA: I can't see you Thursday, I'm busy!
PETER: Miss Barrett, you seem to think there is something wrong up here in your mind that says: he enjoys taking his evenings off and spending them with his clients. No. I'm making a special exception in your case. Because... I respect you. It's corny but I respect you as artist. And as a dresser, too! This is a magnificent coordination you have going here today.
DANA: All right. I'll see you Thursday.
On Peter's second pass at Dana, she finally gives in to his shtick. At this point, the Ghostbusters have become successful, which probably makes her feel more comfortable with Venkman's general weirdness. Also, he's actually come up with some research on her Zuul problem, so maybe he seems more legit. Still, we can't help but wonder if on some level we're supposed to think that she's in some way dazzled with his newfound stardom.