Can you still call a woman "handsome"?

Well, the use of handsome in that film may well be archaic or it may not. According to NOAD it currently means

handsome (of a woman) striking and imposing in good looks rather than conventionally pretty.

What I think it doesn't mean is hot in the sense we would use it today. The emphasis is on striking: she's not conventionally pretty, but neither is she ugly. She has striking features.

Here is someone I think would fit the bill rather, er, handsomely:

And here is someone who is more conventionally pretty:

But remember the worn adage about beauty being in the eye of the beholder? It's worn because it's true. There are certainly people who find Sigourney Weaver more attractive than Scarlett Johansson. And I can tell you who I would choose in a heartbeat if I were ever in a death match with an alien.

Handsome and pretty are two different types of human attractiveness, with handsome being more rugged and angular, and pretty being softer and more delicate. We tend to associate handsome with masculine beauty and pretty with feminine beauty, but there are also pretty men and handsome women. As alluded to by Brian, the use of the term might not necessarily be viewed as a compliment, since it implies a gender-atypical look.

I don't know about other parts of the US, but in the South it is very common to refer to a lady as handsome. In general it is a term used by older folks. A woman who is handsome has good looks that keep and she may have a certain chiseled quality or ruggedness that is noticed more on men, but is distinctly feminine on her. This is someone who ages well. My grandmother would always point to women 'looking handsome' at church.

I was under the impression that "handsome" was reserved for older (~50+ yo) women. Perhaps used when beauty had faded but the women retained a certain je ne sais quoi. I thinking here of Glenn Close, Sigourney Weaver or Helen Mirren.

That being said, I have not heard the term used for a while.