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.
According to Arnold Schwarzenegger in the DVD featurette "The Future is Coming", this movie was set in 2015, the same year as Back to the Future Part II (1989).
The name was changed from "The Sixth Day" to "The 6th Day" to avoid confusion with The Sixth Sense (1999).
The exterior of the house at the start of the film is the same house seen at the end of Timecop