I personally think Tom Hanks' movie 'That Thing You Do' is far more faithful to the garage band story, than 'Not Fade Away' which as someone stated above is mediocre and a total rock n roll cliche movie.
With Tom Hank's movie, I feel Hank's first hand experienced garage bands, as the clothing, the story and the times are portrayed very well, there is no long haired folks who resemble later rock bands, there is no bell bottoms, the movie is very clean cut, even the guitar amps they use are faithful to the period.... heck there is a scene in the movie where the band cut their demo in a movie theatre and probably is an as realistic account if anything of what The Fenton label recording studio must have looked like at Great Lakes studios.
Another great scene in the movie... was when the band first heard their own song on their local radio station, the scene is what I imagine many bands experienced, especially in the garage genre.
also another thing great about 'That Thing You Do' compared to 'Not Fade Away' no exaggerated drink or drug use.... teens in 65/ 66 were running more on teenage frustration than any drugs, well thats the story told to me from every 50 something American guy I've spoken to.