The thermal coffee mug/bong was a fully functional mug and bong as portrayed in the film, the prototype of which cost $5000 to make.
Much of Drew Goddard's inspiration for this movie came from his own upbringing in Los Alamos, New Mexico, a place filled with scientists and co-workers all going about their business and living seemingly routine and ordinary lives even though they were building nuclear weapons that could potentially destroy the entire world. He talks about this in DVD special features interviews and commentary.
During the lake scene, the only student not to jump into the lake is Marty, who remains fully clothed on the dock. This was partially due to Fran Kranz noticeably being in as good, if not better, shape than the other male students. In the commentary for the film, the writers joke that he was "ripped like muscular Jesus" and assert that if Marty were shown being that fit it would ruin the character. This is partly also why Marty wears baggier clothes than the other students.
During production, MGM saw the dailies of a scene where Chris Hemsworth instructs his friends. On the basis of his performance, they signed him on for Amenaza roja (2012). Two days later, Hemsworth was also chosen to play the lead in Thor (2011). Both Red Dawn and The Cabin in the Woods would eventually be delayed for several years when MGM went bankrupt, and were finally released a year after Thor.
The failed rituals from other countries are references to various classic movies and monsters. The Kyoto ritual is a reference to Ringu (The Ring). Buenos Aires ritual is a reference to King Kong. The Stockholm ritual is a reference to John Carpenter's The Thing. The Madrid ritual appears to reference Dracula.