Wasn't much of a fan of "That Thing You Do"... thought it had a great premise (and I love the title track song), but felt that it was an idea (about what happened to one hit wonders in the 1960s) that really didn't have much of a storyline past the usual "Behind The Music" type of stuff.
I saw it more as self-parodying portrayal of the music industry in the 60s and in that regard I thought it worked to delightful effect. Listing Ethan Embry in the credits as "T.B. Player" (if you pay attention in the film, he's never referred to by his name only ever as "The bass player") was an amusing touch. And there was the overly self-important lead singer/guitarist, Jimmy (played by Jonathon Schaech), the foolish and amusing (overall the comic relief of the entire film) guitarist-- Lenny (played brilliantly by Steve Zahn), and the lynchpin the one guy with the good head on his shoulders-- Guy (Tom Everett Scott).
I also got a kick out of Charlize Theron as Guy's disinterested girlfriend who would rather visit her dentist than go see her boyfriend perform live (a cliche, but done very tongue in cheek in the film).