Although no mention is made in the movie, the character Keyes played by Jake Busey is the son of Peter Keyes, the government official from Depredador 2 (1990) who died during the hunt for the Predator. Peter Keyes was played by Gary Busey, who is Jake's father in real life as well.
When the Predator grabs its mask from the display case, the original Predator mask from the 1987 movie is briefly seen right next to it.
The film was originally conceived as a reboot of "Predator" until Shane Black came aboard and confirmed he would be making a sequel instead, as he wanted to continue to explore the "Predator" mythology.
Shane Black wrote Thomas Jane's character Baxley with Tourette's syndrome because Black himself has Tourette's.
The film was directed and co-written by Shane Black, as a sequel to Depredador (1987), Depredador 2 (1990), and Depredadores (2010). Shane Black played Hawkins in the original film.
Shane Black: [Disarming a gunman] Quinn McKenna takes a gun out of Casey's hand while she holds him at gunpoint. Black's screenplays often feature such scenes, e.g. El Último Boy Scout (1991), Memoria explosiva (1996), and Entre besos y tiros (2005).