The demonic groaning heard when selecting "nightmare" mode is a sample of a woman moaning, played at 1/4 the original speed.
On the underside of the map Q3DM16 (The Bouncy Map), there is an image of the Dust Puppy character from the online comic "User Friendly".
Crash's voice is essentially Slash's voice, slowed down 2x.
The BFG is looked very different compared to Quake 2. In Quake 2, the BFG has a big design, need two hands to carry. While in Quake 3, the BFG is rather small, and fires full auto.