The building at the climax of the movie is the same one used in the climax of True Lies (1994) and many of the shots are similar to this later film.
For a promotional item, there was a pair of boxer shorts, white with Short Time in red written all over them. The scene where Detective Simpson is at the doctors office where he's wearing just boxer shorts and his dress shirt is why they gave away the boxers as promotion item.
Despite a Region 2 DVD release by Carlton International Media UK in 2002, the film was never released on a Region 1 DVD. It only had a VHS and Laserdisc release by Live Home Video in the United States. However, it will play on a computer with a DVD ROM drive. Computers can play any video format and region encoding.
When "Short Time" was first shown theatrically, There's No Disgrace Like Home (1990) was shown before it. The son on The Simpsons is named Bart Simpson, and coincidentally, Dabney Coleman's character in the movie is named Burt Simpson.
The movie played in the break room is Stakeout (1987), that features a car chase which was coordinated by Jacob Rupp and Conrad E. Palmisano, both of whom also worked on this film's chase scene.