In the restaurant, just before Irving farts for the first time there is an old women sitting on table to his left, and a man with blurred face is sitting behind Billy. In the very next scene the same woman is sitting on the table behind Billy and the man with blurred face is gone.
Billy is reading a notice board which has a number of notices pinned to it, including the Carolina Cutie Pie Pageant flyer. Grandpa pulls the flyer off the board, which should have left a small rip at the top of the flyer. When we cut to a close up, there is no rip.
The goof item below may give away important plot points.
When Grandpa and Billy leave the bar at the end of the movie, they knock over the row of motorcycles. The scene cuts to the bikers reaction and then when it cuts back to the car leaving, the first motorcycle is back upright.