My favorite bit of 80s trivia is that when Run-DMC asked Steven Tyler for the lyrics, he didn't know them. He had been performing the song live, and would just kind of ramble and mumble through a lot of it, and so he had to go back and listen to the song to try to remember the original lyrics to write them down. Tyler wasn't 100% sure what he was saying on the recording, and wrote down his best guess.
This was all on his way to the studio to record the song.
Also, when Perry wanted to re-record the bassline for the cover, they realized the studio didn't have a bass guitar. Tyler and Perry had been brought in to re-record their singing, but the rest of the band was not going to re-record the music. MCA of the Beastie Boys happened to be hanging around the studio, and ran home to get his bass for Perry to use on the recording.