The most evident example of "stupidity" is the animals' illiteracy. Except for the pigs, the dogs and the donkey Muriel, the rest of the animals learned at least part of the alphabet but "got lost" along the way. Some never even made it past "D." Whever they tried to learn more, they would forget the first part.
Another example of stupidity is the inability to think in abstraction. When a forum is called to set up rules, only the pigs have any ideas of what laws might be needed in running the farm. The animals resort to symbols to express their new common identity, such as in hoisting the green and white flag (originally a tablecloth), renaming the farm, and singing "Beasts of England." They do no know how to differenciate between symbols and the things they represent.
Related to the above, the animals also have a big problem in their system of logic. They are unable to reason in analogies and can hardly think in terms of categories. When Snowball explains away why chickens are not part of creatures having "Two Legs," they are satisfied with his explanation:
The birds did not understand Snowball's long words, but they accepted his explanation, and all the humbler animals set to work to learn the new maxim by heart.
Rote memorization replaces critical thinking.
The animals' stupidity is perhaps not their fault, but they show themselves to be perfectly inept at defending their own interests even if they are sincere about wanting to "play fair."