When Hannah chews the black gum, her mouth gets all black. When she takes of the wig and talks with Oliver, her mouth is completely clean.
When Hannah is chewing the black gum, after she blows the huge bubble some of it lands on her cheek and the resulting black dot on her right cheek disappears between shots.
When Oliver is hanging from the sky roof, Lilly puts "Hannah's" hat on Miley's head, and Miley's father has her wig, then in the next shot of her she only has her wig on, but then in the next shot she has on both.
When Oliver starts to drop into the limo, Robbie pulls the wig and puts it under his right thigh. However in the next shot, we see Lilly helping Hannah put on the wig from the completely opposite side.
The first time Miley is in the limo and she puts on her seat belt, it is on her shoulder, the camera cuts to Lilly and back to Miley and the seat belt is beside her shoulder.
When Lilly tells everyone her name is Lola LaFonda near the start, her lips don't match what she's saying. The "LaFonda" part was dubbed because she says "Luftnagle" in reality, but this was before the writers decided to keep her alias as Luftnagle.
In the end scene when Miley is chewing gum in front of Oliver, stage lights are reflected in her sunglasses.