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.
I just learned yesterday that Liv Tyler didn't even know Steve was her father until she was around 11 years old. Apparently Liv's mother (a former Playboy Playmate) had a fling with Steve and got pregnant, but didn't want Steve involved in the child's life because he was so heavy into drug abuse at the time. So she said the child was another former lover's child, rock musician Todd Rundgren. Rundgren signed the birth certificate, and paid for Liv's schooling. It's not clear if he was aware that Liv wasn't his or not. When Liv was around 11 years old she met Steve and immediately noticed how much they look and act alike. She confronted her mother who came clean about the ruse. Apparently Steve has been a good father ever since learning that he has a daughter, and they have a good relationship together.
Edit:
I just looked it up and apparently Rundgren realized there was a chance that Liv might not be his, but decided that she needed a father and he would fill that role. What dude being a man.
another bit of trivia is that Run-D.M.C. didn't even know what the song sounded like, yet they had been freestyling over the drum intro at live shows for a while