When Alice grows in the court scene, she says "But I didn't eat the caterpillar's mushroom!" That line was left behind from a deleted scene (based on a scene in the book) in which Alice ate the Caterpillar's mushroom which caused her to grow and shrink.
The Mock Turtle, who says he is what mock turtle soup is made from, is a cow in a turtle's shell. This was because mock turtle soup (for those who couldn't afford to have real turtle soup) was generally made from veal.
The scene with the Fawn (and corresponding musical number) was written to be included in Part Two, after Alice's encounter with the Gnat; however, this was shifted to Part One in editing.