Right after the family parks the car in the Little Miss Sunshine parking lot, Frank immediately jumps out of the car and runs at his fastest towards the entrance of the building to sign Olive up for the pageant.
Dwayne goes backstage to look for his sister:
Pageant Worker: Are you authorized to be backstage?
Dwayne:No.(To Pageant Girl) Hey, where are the dressing rooms?
Pageant Girl: Are you allowed to be here?
Dwayne: Just tell me where the dressing rooms are!
When the family stops at a gas station and Grandpa asks Frank to buy him some porn, "something really nasty" and buy himself a "fag rag". Toward the end of the film, we see what he got; two fairly standard porn magazines, and a gay-oriented one called "Buns & Ammo."
In a phone message from Sheryl's sister Cindy:
Cindy: Sheryl, it's Cindy. Remember when Olive was here last month? She was runner-up in the regional Little Miss Sunshine? They just called right now and said the girl who won had to forfeit her crown. I don't know why, something about diet pills.
YMMV, as it kinda implies an eight-year-old girl was taking diet pills.