Plot hole: Scar tells the pack he didn't make it to the gorge in time to help Mufasa. However Zazu was with them at at the gorge. He could have easily told Serabi or any of the other lions on the numerous times he spoke with them, exposing Scar.
Continuity mistake: When Anna's singing "The next right thing" she puts a bag on her shoulder, with the strap on top of her hair. After the camera spins round her, her hair is suddenly on top of the strap. This bears a strong similarity to the mistake in the original Frozen where Elsa's hair passes through her shoulder - might be a deliberate nod, or else animating hair around objects is difficult enough that shortcuts are often taken.
Factual error: The USA map is inaccurate for the year it is set in. It shows all states but in 1886, many of the northwest states (e.g. Montana, Idaho, the Dakotas) weren't states until 1889+.
Continuity mistake: The two cucumber slices that Jesper puts in the palm of the Drill Sergeant change position between shots - in particular, in the close-up with Jesper walking away and putting the teacup in his hand as well, the two slices are side by side, while they are instead one on top of the other before and after. (00:02:25)
Factual error: With a number of flowers blooming, the movie appears take place in spring. There are many scenes of central park with flowering trees and shrubs in full bloom. However, the yellow blooming shrubs called forsythia do not bloom at the same time as the flowering cherry trees. Forsythias bloom about a month earlier than cherries and are usually the first items to bloom in spring.
Continuity mistake: After the alien abduction, Emmet plans to lead a rescue mission and opens the gate asking "Who's coming with me?" During the sequence, the shadows change completely. At first he is not casting much of a shadow, then it reaches the metal doors, then it stops midway towards it. (00:20:55)
Other mistake: When the characters go to the Himalayas, the whole time, like for 20 mins, including the confrontation scene, they are all wearing casual, short-sleeved shirts. You can see Mr. Burnish's henchmen wearing winter clothing, while the main characters don't freeze to death. They only start getting cold after a long time.
Continuity mistake: The protagonists escaped from captivity and managed to return to Harry's palace. Luka decides to leave to go look for his mother. Harry seems to send him off, and he is standing in the middle of the stairs, about 4 steps below the guard. Harry at this point is in close-up; the guard is not visible, and at the next cut somehow Harry shoves him off as if he were standing directly behind him. (00:16:00)
Continuity mistake: In the prologue, the Nazis storm the Bresson residence. The elder Professor Bresson is sitting at his desk, back turned to them. There's an open fountain pen next to him, right by a paper sheet, but when Bresson answers rather defiantly to the bad guys, the paper sheet suddenly has disappeared. (00:02:15)
Continuity mistake: When Hodaka first fires his gun whilst being threatened by the man, the shell casing lands on the ground beside him, right next to his head. A couple seconds later, when Hina goes to help him up so they can run off together, the shell casing has vanished from the ground. (00:22:06)