There is a gate in the background in one of the beginning scenes, after Sherry initially hurts herself on the clamp. A banner on the gate reads "labor will set you free", just as the gate into Auschwitz read.
Although the movie was filmed in London and South Africa, it takes place in Maine, as most of Stephen King's stories do.
Jim Cummings, the voice of iconic characters such as Winnie the Pooh, Tigger, Darkwing Duck, Pete, Ed the Hyena, Ray the Firefly, Hondo Ohnaka, Dr. Robotnik and a variety of other animated characters, provided the vocal effects for the titular machine and was glad to get to work with director Tobe Hooper, whom he was a fan of, but felt that the strain put on his throat by making the Mangler noises and the quality of the film itself wasn't worth the effort. He once saw the film on television and was amused to see that his name was misspelled as 'Tim Cummings' in the end credits, as it meant that he got paid to do a bad film and no one would even know he had been involved.
Hadley Watson is the manufacturer of the Mangler, it's displayed right on the front. Each of those words have 6 letters in them. There is a big 6 right underneath those words. That's 3 6's. 666 is the sign of the Beast.
Part of the company's name that made the folding machine, Hadley Watson, may be a reference to the sadistic captain of the guards in "The Shawshank Redemption", Byron Hadley. "The Shawshank Redemption" is also a film adaptation of one of Stephen King's short stories, "Rita Hayworth & The Shawshank Redemption", while "The Mangler" is also a film adaptation of one of King's works (the short story of the same name)