Anyway,
this article shows a few of the issues, and I'll add to it (sorry if my rant gets too boring/technical, I have a feeling it does):
There is indeed a large amount of variation that can be obtained by looking at all the sperm of the father (eggs are more difficult to look at en masse). But the 2 brothers they make are so different, from the same parents, that was implausible. Unless (and this wasn't mentioned), they are introducing new genes artificially into the sperm library.
A bigger problem is the fact that almost all "traits" including many diseases are the result of not just several genes with very complicated interactions but also different heritable factors (collectively called epigenetic). An even bigger (and fairly obvious) one is that things like propensity to violence are not strongly heritable.
So, in 1997, when the movie was made, the human genome hadn't yet been sequenced. It was completed in 2003, after 15 years and a billion dollars. In the movie they sequence everyone's genome several times a day. Granted that sequencing is much much faster now, but that speed is quite unthinkable, since it's not just a question of computer power, the chemical reactions needed to identify 3 BILLION bases will take some time. Even if instead of the whole genome they do something like what the police do nowadays and focus on "mutation hotspots" of diversity within the genome ("DNA fingerprints"). (personally with such strong selection for genes across the gnome, I think some of these hotspots won't have quite so much diversity)
Now, the point where we burst out laughing (btw the link I posted was happy with this, they assumed the print out has the interpretation not the sequence):
In one scene the girl gets a print-out (WHY A PRINT OUT??? why not look at a screen? It's going to be a really really long printout) and knows exactly what is wrong with the man. To realise how ridiculous this is,
this is what the sequence of a single bacterial gene (these are much much smaller than ours) looks like. It's like Neo looking at the 1s and 0s of the Matrix and transcending it (except DNA is a 4-letter code), that's how good she has to be to be able to understand anything.