When Alice is riding Bayard towards the Red Queen's Castle, her Bandersnatch scratch is on her left arm, when it should be on her right. Also, the flower that the Mad Hatter had put on her dress was on the left instead of the right. Because the film is flipped/reversed.
When Alice climbs back up out of the rabbit hole, the estate where her party is being held is visible in the background. Many of the guests appear to be dancing, yet when Alice returns to the gazebo, all of the attendees are waiting for her exactly as she left them.
When Alice takes the Bandersnatch's eye away from the Dormouse and holds it in her giant-sized hand, the size of the eye increases from about the size of a marble to about the size of a baseball. When the Dormouse had the eye tied to her belt, the eye should have been about the size of a baseball (the size of the Bandersnatch's other eye).
When they are lining up before going into battle and are waiting for Alice to arrive, the reins of the White Queen's horse are hanging down. The shot cuts to the White Queen and Alice talking. When it cuts back to show the horse the reins are over the neck of the horse.
When Alice is jumping over the heads to get to the Red Queen's castle, she sticks her foot in a puddle, clearly getting it wet and even shaking excess water off. However, in subsequent shots, her foot appears to be completely dry.
When Alice eats the sweet bar labeled "Eat Me" to get herself enlarged and be able to pick the key from the table and starts growing. The camera first takes the shot from up and her thighs can be seen coming out of her skirt as she grows bigger. The shot continues from the front and it shows the dress getting shortened again from the knees and her thighs coming out.
Right before Alice rides up to the White Queen on the Bandersnatch, the Queen has steps next to her horse, presumably to help her climb on. However, when they begin to march away to battle, the stairs simply disappear and the Queen is on the horse. Who moved the stairs?
After riding Bayard to the Red Queen's castle, Alice has to jump onto floating stone faces to get over the moat. On her final jump, there are several faces left to get to the other end, yet after jumping she ends up on solid ground on the other end.
While looking at the scroll, the Red Queen says she would recognize Alice anywhere by looking at her hair. Yet when Alice is in her castle under the name Um, why doesn't the Queen realize it's her? It is entirely within the Queen's character to claim she would recognize Alice, and then later not actually do so. She also believes that all of her court members have overly large features when the rest of the characters know they are fakes. There are multiple evidences throughout the movie that the Queen is easily deceived.
The White Rabbit is shown in at least one scene with pads on his feet like a dog or cat. Real rabbits do not have pads on their feet, nor do they wear waistcoats, obsess about time, or get involved in politics. But as this is a fantasy rabbit, it is entirely feasible.
The goof items below may give away important plot points.
At The Mad Hatter's beheading, the executioner moves the ribbon away from The Mad Hatter's neck. In the next shot from the beheading stage, the ribbon is in the same position it was before it was moved.