Factual error: When Sherrie and Drew are in Tower Records, the background song is I Remember You by Skid Row. But that album wasn't released until 1989, and the movie is set in 1987.
Suggested correction: The movie also says that Drew wrote "Don't Stop Believin" when the song came out in 1981. They also sing Heaven and More than words which didn't come out until 1989 and 1990 respectively. It's a musical that's full of 80's music, so they pulled all sorts of 80's music. It's not a mistake to have songs show up in a year, in a completely made up timeline.
Factual error: Tom Cruise throws the new Rolling Stone magazine at Paul Giamatti in the latter's office and tells him to look at page 68. Giamatti looks at and starts reading from the right hand page, but in magazines page 1 is the front page, and therefore subsequent pages on the right are odd numbers.
Factual error: In the Bourbon they use moving lights which were first used in 1980 actually the ones used were first produced in 1998.
Factual error: When Sherrie steps off the bus in L.A. you see the Hollywood sign, the Capitol Records building and the Roosevelt Hotel in the background. These landmarks are nowhere near each other.
Factual error: There's a poster on Drew's bedroom wall featuring the cover of Not Fakin' It by Michael Monroe, but the album wasn't released until 1989, and the movie is set in 1987.
Factual error: The Hollywood sign is shown as a tourist attraction with platforms, steps, and railings, but in real life none of these features exist and the area is gated and definitely off-limits to the public.
Factual error: In the scene where Drew and his bands are seeing up on stage you get a clear sight of the drums. The drummer has die cast hoops on his drum set which did not come out till early 90's.