The events of Insurgent pick up within days of where Divergent ended; in fact, Jeanine's hand was bandaged throughout Insurgent, yet in just a few short days Eric's hair has grown in and he is able to run full-speed through the woods, even though Tris shot him in the leg during the attack on Abnegation.
During the first chase scene through the woods, the heroes jump over some tracks and run beside a double width train. The bad guys, on the other side of the train, continue to fire at the heroes. You can see the heroes, again on the far side of the train from those that are firing at them duck as sparks fly from bullet impacts into the train cars. The bullets would have had to fly through two metal cars full of produce and hiding Factionless to emerge on the heroes side.
During the second day that Tris is going through the simulation, Jeanine is briefly seen wearing the dress she was wearing the day before, the scene cuts to another simulation, and once it cuts back, she's wearing a different dress.
As Caleb, Four, and Tris are being chased by the Dauntless vehicles from the Amity compound, the distance between the vehicles and the runners constantly changes. The initial camera angle above the compound shows a Dauntless vehicle not too far from the runners. The next camera angle shows the runners outrunning the Dauntless vehicles [which in the previous scene had outpaced some Dauntless guards chasing the runners] and widening the gap. Then the next camera angle from above again shows the distance between the runners has decreased, yet the runners are STILL able to outrun the Dauntless vehicles and escape into the woods.
Towards the end of Tris's testimony under the truth serum, she looks at Four. On Four's right is a guy with a headscarf, but when the scene shifts back to Tris and then to Four again, the guy is on Four's left side. The scene is flopped.
When Tris is given the truth serum by Candor you can clearly see the hypodermic needle moves on her neck indicating it is a prop and not actually inserted into her neck.
When Tris is in Candor HQ while it is being attacked, she is shot at by multiple armed assailants and dashes through a door. The bullets from the guns punch through the thick metal doors. A few moments later, the men open fire on the members of Candor. Tris inspects the wounds and notices that small objects are now embedded in their skin with absolutely no skin irritation or mark. The men did not reload or change weapons at any time.
when Triss is telling Jack Kang that her mother and father died Four has a man standing to the left of him but after Triss admits to killing Will the man is standing to the right of him.
In the movie Divergent, Tris only has one tattoo, the three birds on her chest. In Insurgent, Tris now has a tattoo on her right shoulder.
Caleb constantly mispronounces Erudite, as if it were spelled areadite. While this might possibly be normal for other characters, since Caleb actually is an Erudite, he would pronounce it correctly.