Other mistake: When Glen Holland hears that John Lennon was killed, he is sitting at his piano and outside the window it is sunny and leaves are on the trees. As he walks home, it is overcast, snow is on the ground, and the leaves are off the trees. Since Lennon was killed in December of 1980, the latter "weather" would be correct.
Other mistake: At the beginning of one of the school years, there is a sign on the front of the school that says, "Welcome back Class of 1980". A few months later, in December of that same school year, John Lennon is murdered. Since that class is graduating the following spring, the sign should have read "Welcome back Class of 1981", not 1980.