Yeah I have that first poster hanging in my room right now. Took me forever to find that poster (ended up going on E-bay), but I digress.
There used to be a gigantic list of little symbolism things in Gattaca on the internet. I've since lost track of where it was and what it exactly was, but somethings that I still remember that was kinda cool. The most simple and obvious one is probably how Gattaca is all composed of the elements that make up DNA, guanine, adenosine, thymine, and cytosine. I remember learning about this in Bio, and at the time I remembered that for every G, there's one C and for every A, there's one T. So I looked at the title, and was vaguely disappointed that there were three A's in this movie and only two T's. Bleh. Just one of those things.
Anyways, Eugene which means "well born" is also something prominent (since Jude Law's character is well born). As well, eugenics is the main theme of the movie.
Other things that are interesting are how the staircase is shaped like a double helix (the shape of DNA) and Irene Cassini, Uma Thurman's character is named after Jean Dominique Cassini, a major contributor to the discovery and further continuation of Saturn (discovery of the space between the rings, as well as several other moons etc). Vincent Anton Freeman (notice his last name) and names in general in Gattaca I think, are also rather important.