Not Your Average Damsel
Far from your usual damsel in distress, Dana Barrett is a love interest with a brain. According to Sigourney Weaver, the all-male screenwriter crew originally conceived Dana as a model, but when Sigourney was brought on board she had a few notes.
By the time Sigourney was done, the character went from a hot model to an intellectual cellist. The character change is great not only because it avoids a cliché, but also because it makes Dana a more formidable adversary for all of Venkman's weird attempts at flirting.
Like how about this classic interchange...
DANA: You know, you don't act like a scientist.
PETER: They're usually pretty stiff.
DANA: You're more like a game show host.
She's got that one right, right? Midway through the movie, Dana is finally charmed by Peter. Maybe it's because the Ghostbusters are famous and successful by this point, but Dana doesn't seem like the kind of person to be dazzled by fame.
It seems like Peter finally scores the date because (a) he brings Dana some helpful info on Zuul, and (b) she can't help but laugh at him. Here's the bit that finally gets her to hesitantly step onto Venkman bandwagon:
PETER: 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.
Venkman might be delivering stuff about respecting her kind of facetiously, but the thing is that it's probably actually true. There does seem to be something about Dana that attracts Peter more than young co-eds he's usually chasing. We figure Dana detects that somewhere under all his sleaze-tinged quirkiness, there's actual sincerity.
Also, Peter's impulsiveness might just be a breath of fresh air for Dana. The only other guy we see her with is a stuck-up looking violinist with a penchant for nose spray.
P.S. It's a not-so-open secret that Sigourney Weaver and Bill Murray absolutely loathed each other during filming. That might explain why their romance is so tension filled, and why Reitman, genius that he was, chose to focus on the comedic aspects of their dislike rather than a more conventional romance.
It Ain't Easy Being Zuul
Even though Dana bucks a lot of damsel in distress clichés, after she's possessed by Zuul she does indeed end up being rescued by our knight in shining armor, Peter Venkman.
Still, the movie manages to give us a more interesting riff on this classic storyline. When Venkman shows up at Dana's apartment and finds her possessed, it's Zuul/Dana that tries to aggressively seduce him and not the other way around. The movie also throws in a twist when Peter finds Dana turned into a horned terror dog bent on his destruction when he comes to rescue her.
In the end, we get the classic knight in shining armor scenario, with Venkman rescuing Dana from the jaws of death and even carrying her off of the roof in a classic pose. And as Venkman's reward, the damsel gives him a great big kiss in front of the cheering crowd.
Oh, whatever. Whether it's classic or cliché, we still want these two to get together in the end.