Early in the movie Alice directs her crew to heel to port. Visually, the ship heels to starboard.
The chess board (on both sides of the looking glass) is set up incorrectly, with a dark square at lower right rather than a light square.
As a child the Mad Hatter has his adult teeth but no gap between them. He also has no lisp. As an adult, the Mad Hatter has both a gap between his front teeth and a slight lisp. However, even in humans such changes can sometimes occur (e.g. due to injury), let alone in a weird magical being like the Hatter.
The princesses are depicted as having blue/green eyes as children, but with dark brown eyes as adults. However, the eye color can change over the years, under some specific conditions, even in humans, let alone in mysterious magical beings like Mirana and Iracebeth.
Alice lives in London, UK. The Wonder, her ship, has the American flag on it. However, many ships are registered in countries other than that in which the owner (or owning company) resides. This may be for tax or other reasons.
When the doctor attempts to give Alice a shot, he depresses the plunger to remove the air bubbles. In the following scenes, you can see that there is clearly a significant amount of air remaining in the syringe.