Freddy Fazbear and his variations are Killer Robot bears with huge references to Freddy Krueger, such as the name and their tendencies to harm children. Aside Fazbear, the franchise is also riled up with the serial killer references.
The words in the fourth promotional picture (No place to run, and exactly one place to hide.) is an obvious spin on the lyrics to Martha Reeves and the Vandellas' "Nowhere To Run".
And on another note, "No place to run" is a name of an album by the band UFO.
The minigames are obvious shout-outs to Atari 2600 (and its competitors') games.
One of the names for the Custom Night, for activating only Foxy and Mangle, is called Foxy Foxy.
And speaking of Foxy, the theory that he was inspired by Sweet's "Fox on the Run" is only strengthened by Mangle — it has a pretty face, but the rest of it is out of place; it looked all right befoooooore…
The "Something borrowed... Something new..." teaser might be a reference to the TLC TV Series of the same name.
The Nightmare animatronics may reference another horror movie franchise — A Nightmare on Elm Street, whose villain is also named Freddy, and also involves ghosts, child murders, and revenge. It almost has the feel of Scott taking the Nightmare on Elm Street jokes and running with them for the last game.
Although not in the game itself, the filename of the October 22nd Halloween DLC teaser image, which teases Nightmarionne , is "dontwakethebaby.jpeg", which is a shout-out to Markiplier's nickname for the Puppet in his playthrough of the second game.
Another possibly unintentional reference goes to the Saw films, namely the first movie. Funtime Foxy's gimmick taking place in a dark room that you can illuminate with flashes of light is similar to a scene where Adam is looking through his darkened apartment, using the flash of his camera to navigate.
One of Springtrap's kill taunts is "Bittersweet, but fitting...", a shout-out to the WWI poem Dulce et Decorum Est, which describes one of the worst horrors of war — death by chlorine gas.
Hanging next to the right vent is a drawing of a screaming clown. It's a dead ringer for the redesigned Pennywise in It (2017).
Soon after starting the game, you can overhear Roxanne assuring herself, "Your hair is beautiful." Very much in keeping with the extremely '80s theme.
The Daycare Attendant seems to be a reference to the sun/moon backup singers from The Rockafire Explosion.
Given the PizzaPlex's Retraux aesthetic, it's probably not a coincidence that one of the main animatronics is named Roxanne. She's also very likely a reference to a certain other very 80s member of a villainous trio named Roxy, who looks similar◊ and has similar Hidden Depths to boot.
Roxanne— a wolf— also has a voice line where she asks "are you hungry?" Hungry like the wolf, perhaps?
Of all things, climbing inside Freddy has a similar animation, with boot-up sequence and all, to boarding a Titan.
During the Arcade segment, the facility's public-address system can be heard declaring "Reticulating splines".
During the Fazerblast sequence, the "alien" S.T.A.F.F. Bots may declare "Resistance is futile."
In the opening sequence, Freddy singing while holding the mic and its stand pays tribute to the late Freddie Mercury, who also did the same while performing. They even share similar names.
So the animatronics can be stunned by camera flashes, you say?
One customer complaint notes that some of the pizzas in the restaurant have strange appearances in terms of how they're sliced, leading them to believe the place is recycling leftovers to make new pizzas out of. This references a similar conspiracy surrounding the actual Chuck E. Cheese's, which was determined by Food Theory to simply be the consequence of using a very dull rocker blade to cut (regular) pizzas.
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