Corrected entry: When Max goes to enter Barter Town, he's stripped of his weapons (save for the dagger hidden in the handle of his fly swatter), because, as he's told, "It's the law." When he confronts Master Blaster, about twenty weapons are trained on Master Blaster to subdue them. Unless it's part of the plot to get rid of Blaster, it is an inconsistency.
Corrected entry: Near the end of the movie when Max and the gang are in underworld, the guy with the mask hanging above his head gets knocked into the pig poop, gets completely covered and also loses his mask. Later in the next scene, he is not only cleaner but has his mask back and completely clean with no traces of ever being covered in poop. In the film he should not have had enough time or water to clean up.
Corrected entry: The truck they escape on at the end is powered by steam - we can see the funnels and the boiler fire in lots of shots, but nobody during the entire chase feeds the burning boiler with anything to keep the temperature up to boil the water to create the steam.
Corrected entry: In the first half of the film Savannah has very short hair. When she, Max and the children enter Bartertown she has a long pony tail hair until the end of the film.