Continuity mistake: The speech that Moore claims/shows then NRA president Charlton Heston giving in Colorado is actually several speeches edited into one. Note how Heston's clothing changes between cuts during this speech.
Revealing mistake: When De Silva's men start to celebrate after they start building the ramp and the Zealots throw boulders down at them from Masada, the boulders bounce after hitting the ground. Big boulders like those should definitely break, not bounce.
Continuity mistake: When you see Heidi get her food in the restaurant, she is holding one food container. Later you see her with two (without picking another one up).