When Sarge uses the severed hand to open the advanced weapons armory, the computer voice (and subtitles) say, "Welcome, Dr. Patricia Tallman." The character is named in the credits as Dr. Hillary Tallman. Much like the inclusion of John Carmack's name, this is a subtle insider reference, but one that is arguably more likely to be noticed than the name of ID Software's infamous co-founder Carmack.
The hand held video game Duke is playing (Galaxian 2 by Entex) is meant to be played holding the game vertically, one side of the buttons control the ship, the other side the Galaxians. Duke is holding the game horizontally, playing both sides at once, while seeing the action sideways.
What are the differences between the theatrical version and the unrated version?
In comparison with the R-rated theatrical cut, the unrated version runs more than 6 minutes longer adding more action and story to the film.
A detailed comparison between the theatrical version and the unrated version can be found here.
Are there Demons/Hellspawn?
Whilst some of the creatures in the film look like their counter-parts, in Doom 3, there is no direct reference to Hell or alternative dimensions. The creatures were explained to be genetically mutated humans, due to an injection of a 24th Chromosome. Although in the cast listing it does show an actor listed as a "Hellknight" which were the names of the creatures in Doom 3