Continuity: When Ethan Hawke and Uma Thurman are escaping form the party, the sleeve of Ethan's suit is ripped under the armpits when he hits the cop but in a few seconds you see his sleeve completely fixed.

Visible crew/equipment: In the scene where Ethan Hawke is picking out a suit and shoes you see a distinct hand on the left side of the closet holding up what must be a false wall.

Revealing: In the scene where Jude Law needs to pull himself up the flight of stairs to reach the intercom, you can see him use his hips, despite the fact that he is paralyzed from the waist down.

Revealing: In the scene where Anton and Vincent are swimming, the distance between the waves is way to short for it being an ocean. It is a pool. Waves in an ocean can not be as narrow as these - they would always have a larger space between them.

Factual error: When Vincent and Jerome are at the Gattaca building at night, they watch a rocket launch. The exhaust from a such a rocket would have lit the area around them or at least the nearby mountains bright as day.