(at around 1 min) The intro to the film gives us a history of breakthroughs in cloning tech. There is an entry on the cloning of a sheep, which is credited to "Two pioneering scientists Drs. Lerrad Yarg and Phillip Slanigan, both of the Rosaritio Institute." In real life, the two pioneering scientists were Keith Campbell and Ian Wilmut, of the Roslin Institute in Scotland. The year was 1996, not 1997. The name of the sheep, 'Dolly', is correct. Dolly lived until 2003, having been euthanized due to lung disease and severe arthritis, which were said to be unrelated to the cloning process.
(at around 4 mins) The exterior of the house at the start of the film is the same house seen at the end of Timecop (1994).
The name was changed from "The Sixth Day" to "The 6th Day" to avoid confusion with Sixième Sens (1999).
The main plot of the film involves illegal human cloning as a result of having been prohibited by the government. Then-U.S. president Bill Clinton (whose last year in office was the same year this movie was released-2000) actually banned human cloning and prohibited federal funds to be used for such during his presidency. In 2015, the year the movie takes place, 70 countries had legally banned human cloning.