Trivia: Ash's car has appeared in most of Sam Raimi's movies. Look out for it in Spider-Man and Darkman.
Trivia: The disbelieving clerk Ash is explaining his adventure to in the S-Mart ending is Ted Raimi, who can also be seen in the crowd below the castle battlements receiving Ash's pep-talk just before the battle with Bad Ash's Army of Darkness. Ted is director Sam Raimi's brother--and is best known for his part as Joxer in the Hercules and Xena TV shows (of which brother Sam was executive producer) where he again worked with Bruce Campbell.
Trivia: When Ash opens his trunk to get out some useful items, there is a Fangoria magazine and the cover is for Army of Darkness.
Trivia: When Ash calls Wiseman Joe "spinach chin," it's a reference to the classic Three Stooges short Malice in the Palace (1949), in which Moe Howard calls a man with a long beard "spinach chin."
Trivia: Bruce Campbell says that in order to make it appear that the chainsaw was always running, tobacco smoke was pumped through a tube that was slid up his right pant leg, up his shirt, and into the chainsaw.
Trivia: Ash speaks the words, Klaatu Varata Niktu, this was paying homage to a film called The Day the Earth Stood Still. The words in that were Klaatu Barada Nikto (only slightly different), they are spoken by one of the humans (at the request of Klaatu) to Gort (Klaatu's robot) after suffering a potentially fatal injury at the hands of humans, to prevent Gort from destroying Earth. The tenuous link, therefore, is that this phrase must be spoken precisely to prevent the end of the world in both films...
Trivia: The army of the dead is basically made up of mostly skeletons, but in some of the scenes where they couldn't use stop motion for obvious reasons, they have real people standing in with skull masks. (01:02:30)
Trivia: The Magic words that Ash said (Klaatu, Barada, Nikto) are also the names of three aliens on Jabba the Hutt's barge in Return of the Jedi, which in turn took the words from The Day the Earth Stood Still.
Trivia: AOD has 2 different endings, the one where he goes back and fights the zombie lady in S-mart, and the original one where he swallows too much juice and ends up in an apocalyptic future, they wanted to use the original ending but Universal wanted a more audience friendly ending, and they didn't want Ash to be such a anti hero so they changed and deleted a few other scenes. They released the original version to some countries.
Trivia: Bafflingly, despite having little sex or profanity, and only minor cartoonish violence, the film was slapped with an NC-17 rating when it was first submitted to the MPAA. Everyone involved with the film was shocked. Turns out, a single 1-second shot of a little black, blood-like goo splashing onto a wall following a decapitation was the reason the MPAA gave the film an NC-17. Once it was cut, the film was reduced to an R.
Suggested correction: While it's true that it initially got a NC-17 rating, it wasn't because of a 1-second shot of goo. It was mainly for the decapitation scene and ostensible gore. Director Sam Raimi trimmed down the decapitation scene, but refused studio pressure to trim the movie down to a PG-13 rating, so most of the people involved in the actual making of the film weren't expecting a PG-13 rating.
The one-second shot was from the decapitation scene you mentioned. It's the shot the bloody goo splashing on the wall after he slices the hag's head off. As for the second point, upon looking around, I'm finding conflicting reports. I've only really seen one or two sites saying Raimi "refused" to trim the movie down, and many more that imply he tried to appease them for a PG-13 and had no reason to believe it would be rated R/NC-17 due to how cartoonish the film is (several of these sites also cite a book as evidence, but I can't find the book online). But given there are conflicting reports, I'll edit out the last bit.