Revealing mistake: When Joe blows up the Eiffel Tower in Paris at the beginning, it smashes into the Arc de Triumph which then shatters. But as bits of the building go flying off into the Seine River, they bounce off the hard surface, showing it to be plastic not water.
Revealing mistake: Although the movie is filmed with puppets on strings, their movements and their surroundings are made to look as realistic as possible. This nitpick shows a moment when that doesn't happen. As the terrorists begin shooting up Paris, one terrorist runs down the street (in front of the bakery) as citizens run in every direction. One puppet (a female wearing a dress with yellow and white stripes) runs off camera to the left. After she runs out of the shot, the shadow of the puppet appears on the building corner (left side of the screen), being lifted up and out of the scene.
Revealing mistake: In the fight between Team America and the F.A.G., Samuel L. Jackson gets his head kicked in two. You can see that his head is already cracked before he gets kicked. (01:24:10)
Answer: Without giving a timecode, I can tell you that it's during the third act, when Team America has already been freed from their prison cells (in North Korea), and are fighting through the F.A.G. defenses.