Revealing mistake: When the black singer of the band of the nightclub can't perform, Dewey steps up to prove his worth. When he starts getting really into it, he joins the piano player in playing some tunes. You can see some keys playing, but they are not being touched by either person.
Other mistake: Two mistakes in one scene. Continuity Error: As Dewey's father is dueling with Dewey with a machete, Dewey's father cuts a ladder in half. Later in the same scene, you will notice that the ladder is whole. The second (Revealing Mistake) shows a wire leading up from the barn floor to Dewey's father's bottom half, supporting the effect.
Other mistake: There are two mistakes in one scene. First (Continuity Error): As Dewey and Nate duel with machetes covered with sheaths, Dewey swings back hard, dislodging his sheath, and it goes flying behind him. Note where it lands - behind a barn post. After Dewey cuts his brother in half, the shot shows behind Nate, and you are also facing the front of Dewey. Notice the new position the sheath is in - just behind Dewey instead of behind the barn post. Second (Revealing Mistake): After Nate is cut in half, and the shot shows behind Nate talking to Dewey, notice the wire that leads up from the barn floor supporting Nate's bottom half.
Continuity mistake: As Dewey's parents are dancing to Dewey's song on the radio, take notice that Dewey's mother gets her foot wrapped up in the electrical cord of the radio and falls out the upstairs window. Upon her hitting the ground, you should be able to see that there is no cord wrapped around either foot, or a cord that leads back up to the window. However, the radio's electrical cord comes out of the wall socket anyway as if it was still attached to her foot, causing the radio to go on the same journey as she did.