Arrowsmith is the name of a 1925 novel by Sinclair Lewis, but it has nothing to do with the band name. Joey Kramer came up with "Aerosmith," which was rejected by one of his previous bands.
The entire band entered rehab in 1986. They made a very successful comeback when they got out.
In the 1970's, Grateful Dead guitarist Jerry Garcia called the band the druggiest people he'd ever seen.
They were the first big Rock band to appear on The Simpsons as themselves. They were in the Flaming Moe episode in season 3. As part of the deal, Aerosmith's manager had to be drawn in as well, which he was.
The members of Aerosmith have the doors to their dressing rooms decorated including a sign on Joe Perry's door that says "The Admiral is on Board."