The motorbikes with sidecars used in the chase are a playful homage to Indiana Jones and the Last Crusade, in which Indy and his dad escape on a motorbike with almost the same configuration. See more...
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Deliberate "mistake": Right before Rick grabs the half of the broken dagger, he is starting to stand up, only to be kicked by the Dragon Emperor and slid back about 8 feet. As he starts to stand again, you can see that the background is exactly the same as the first time he tried to stand up- meaning that both moments were taken from the same shot, despite the fact that the background should now be different.
Continuity: During the "final confrontation", after Alex wakes up, we see the Dragon Emperor hit Rick with a spinning kick, knocking him to the ground. As Rick falls, in the first shot the Dragon Emperor lands and is facing away from Rick, in the second shot (where we see Rick hit the ground) the Emperor is already turned back to face Rick, and in the third shot, the Emperor turns to face Rick yet again.
Deliberate "mistake": When the Dragon Emperor is giving his Terracotta army the speech near the end, you see a shot that pans across the faces of several of his soldiers. A few shots later, this exact same shot is played in reverse. It is very easy to tell if you look at the way the camera moves up and down to catch the different faces.
Continuity: When the group enters Shangri La, Alex runs down toward Zi Juan and the fountain. Before he gets there, we get to see wide shots from behind him of the ground to his left which is rocky with no path, and we also see that no-one is following, yet in the next shot from the front, Zi Juan's daughter appears instantly to block her mothers sword swing. There was simply not enough time between shots for her to accomplish this, and even if it were possible, her mother would have seen her approaching.
Plot hole: Zi Juan tells the rest of the group when they are in Shangri La that she will take the first watch at the entrance and guard against the emperor getting in. A few shots later, she then decides to have a conversation with her daughter nowhere near the entrance, and now with no-one guarding, means he gets in unchallenged.
Revealing: Just before the final battle, as the O'Connells are preparing, you see Rick and Evie emerge from behind a rock with guns in hand and cautiously watch over what is happening. In this shot, Evie is holding two pistols, and you can see that one of the pistols (should be on the viewer's right) has a bent barrel, revealing it to be a prop of some sort.
Continuity: When Rick and the Emperor are fighting in the end, while they are punching and kicking each other, the Emperor suddenly turns around and is hitting Rick with the back of his elbow after one cut, but if you watch closely, you can tell he didn't have time to turn around, nor did he even start to turn- he simply has turned 180 degrees between shots.