Factual error: We're told they carbon dated the gold to determine its age. Problem is, the gold hasn't aged by the normal processs - as it's been brought forward in time it will appear to be extremely new. As such carbon dating wouldn't work. Also, carbon dating only works on things that were alive and absorbed carbon-14; gold, having never been alive, could not be dated this way.
Other mistake: When the man is in front of the Senate committee asking for appropriations for the Time Enforcement Commission, he states that you can not go into the future as it has not happened yet. During the scene with Atwood scanning the USA Today, the date on the paper is October 30, 2004. So, one could assume that this is the current date. Later on in the movie, there is a news report on the television with the woman stating that McComb's campaign might be denied federal campaign matching funds, and that McComb might have to withdraw from the race. Now, being that the election is only three days away on November 2, 2004, it would be a little too late to withdraw from the race, not to mention the lateness in the determination if he is eligible for federal campaign matching funds.
Revealing mistake: Near the beginning, when Van Damme goes and arrests his former partner, watch when they both jump out the window. It is clear that they are on a cable decelerator. They fall straight down and in a controlled and slightly slowed motion. Very noticeable.
Continuity mistake: When Atwood is sent back and continues his fall, he lands on a black police car with his head and body lying on the bonnet face down. From the overhead shot his body has completely disappeared, as he was wearing a light grey suit which would stand out on the black car.