When Vincent is confessing to Irene, he tells her he doesn't have 20 or 30 years, his heart is already 10,000 beats overdue. In an average male this would only be about 2 1/2 hours, not several years as the story suggests.
When Vincent alias Jerome has his interview at Gattaca you can see that the machine clearly shows a GNQ of 9.8612. When Irene gives the hair sample away for analysing, the woman at the counter states "9.3, quite a catch".
After Irene and Vincent have sex, you can see that the bedroom walls are pure glass (including the corner of the house). You can also see a view of the beach and ocean. Later when Vincent is on the beach scrubbing himself with sand, the house is viewed from the beach. At that point you can see pillars in between pieces of glass on the house, including the corner.
Using hair/eyelashes for genetic testing will fail if no follicle is attached, but this method is used when no other material is available or the information is being obtained surreptitiously (as Irene and the investigators are doing when they use this method). Urine is not the most efficient way to perform genetic testing when other samples are readily available, but the urine test was also performed to look for drug use as evidenced by Eugene's sample failing when he was drunk. More specifically, urine itself does not contain DNA, but it may contain epithelial cells, which do contain DNA. Most healthy individuals, however, do not excrete epithelial cells in their urine. http://www.biology.arizona.edu/human_bio/problem_sets/DNA_forensics_2/06t.html
In the beginning when Vincent is putting the blood into the fake thumb he puts it on his left thumb but he always uses his right hand to get tested. This is because Vincent himself is left-handed, but Jerome is right-handed so he had to make the switch when he assumed Jerome's life.
When Jerome starts to crawl up the spiral stair, he moves his legs with his hands as he is supposed to be paralyzed. However, a moment later his legs can be seen slightly moving when he is struggling to get upstairs.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
After Jerome becomes paranoid about being accused of murdering the Mission Director, he states that the Mission director was beaten until unrecognizable. Towards the end, the detective looks at the body again in the morgue and the face is completely intact. The director's face was covered with blood/matted hair after being beaten. By the time he was in the morgue, the body had been cleaned and the flesh reassembled.