I think unless the parents were fans of the book it's a bit odd to me. And most people will assume that the parents know the book, not just the movie.
I find it to be pretentious. The name only has one, very well-known association (which is not a particularly positive one, in my mind).
Gatsby is not the most honorable namesake, and I'm surprised that anyone who has seen the film would actually want to use the name. I haven't seen the film, of course, so maybe it does not portray the book too accurately.
Another vote against. I think it would come off as pretentious because it would be impossible to remove the association from the character--it's so ingrained.
I agree that it would go over better if it was a nod to the novel as opposed to the film. Jay Gatsby not being the best namesake ever but I know of a friend who has always held onto the name for a future son as she is a huge Fitzgerald fan. I think she is second guessing it now that the movie has come out though, it will likely become a bit of an unfortunate trend name now.
I think it's too tied to the character to work. Maybe as a middle name but it's not really my style. Jay would work better, or one of the author's names.
Baz Luhrmann is a genius.
See, for me this name is dependent on a few things. Based on your reasons, that you saw the movie and think it would be a cute name, no, I wouldn't name your son Gatsby. However, if you proceeded to read the book, fell in love with it, pursued other works of Fitzgerald and/or books set in the same time period/about the same things/American classics/whathaveyou, and then named your son Gatsby, I'd say go for it.
With the first reason, that you liked the movie, then that's all you have to tell people when they ask why you named your son Gatsby. "Oh, I saw the movie when it came out, and thought it was simply wonderful!" While it's not a bad cultural reference, you didn't do a whole lot of research, and named your son after a fictional, obsessive bootlegger.
If you got into the literature and the core of that little sect of culture, then you'd be giving your son a name that is representative of American Gilded Age literature. The name isn't the problem; it's your intention, and how you will explain it.
Of course, if you really love the name, please use it. It would just make us all feel better if you'd read the book.
Gatsby has been on my list for a long time, but for a girl only.