Black Sheep Hit: Multiple times, with "Dream On", "Angel" and "I Don't Want to Miss a Thing". They actually refused to play several of their songs in concert for years because of this.
Coincidentally, Mark Chesnutt's cover of "I Don't Want to Miss a Thing" was a black sheep hit for him around the same time, as he was mainly known for his traditional fiddle-and-steel country, not covers of rock power ballads. In fact, said cover was by far his biggest hit.
The rhythm guitarist is Brad Whitford. The West Wing's actor is Bradley Whitford.
Joe Perry shares the same name with an NFL Hall of Fame running back for the 49ers.
Throw It In: In "Nobody's Fault" you can faintly hear a squeaky door opening during the song's guitar introduction, just a few seconds before the rest of the band starts playing - according to Steven Tyler, this was due to a recording engineer unceremoniously walking in on a take, and the band left it in because they thought it was funny.