Continuity mistake: When JB dreams about singing "Master Exploder" in the small bar, he points at one guy in the audience and literally blows his mind. When he starts pointing you can not only see JB's face, but also how his elbow is in a slight angle. In the next shot the camera shows the guy JB is pointing at and his elbow is completely stretched. The views change several times and the angle of his elbow changes after every cut, until the guy's brain is finally blown out.
Revealing mistake: During the big chase, watch closely when the car goes over the ramp and does a flip. As soon as it lands, you can catch a brief glimpse of a partially-destroyed film camera (covered in black material) rolling along the ground. Its position on the road lines up with one of the previous shots, so it's definitely a camera. (It looks like the car landed on it and threw it along the ground).