The White Rabbit is made from seemingly a real, taxidermied rabbit, with wide, staring glass eyes to boot. He also personally cuts off people's heads for the Queen.
Between Alice being thrown out of the White Rabbit's house and meeting the Caterpillar, she is locked in a storage cupboard with eggs that "hatch" to reveal animal skulls, a loaf of bread that suddenly sprouts steel nails (blunt side out), a tin which Alice only discovers upon opening it contains live beetles, and a slab of raw beef that crawls from one jar to another.
The Caterpillar is a living sock that finds huge eyes and teeth to attach to itself, and always looks as if it's ready to Eat the Camera. It ends its scene by spitting out its own teeth and sewing over its own eyes.
In one scene, as in the book, there is a crying baby that turns into a squealing pig. The unnerving part is that sometimes the pig squeals are combined with the crying sounds.
summarized the film as "a masterpiece of surrealism that's more Tim Burton than Walt Disney." Burton did indeed make his own version, many years later, though it's nothing like this film.