When sitting at table, a man tries to take Kaspar's hat. Kaspar's left hand changes between shots.
After Kaspar is left in the town square, there is one shot of him where the way he holds the note, and the way the bandanna is tied, that is different from before or after.
In a brief scene we see a stork eating a frog with its legs tagged (ringed), but bird ringing didn't start until the end of the nineteenth century, decades after the life of Kaspar Hauser.
In the autopsy scene, the operating table is equipped with an exhaust pipe which is white and smooth. Plastic was not known at the time and pipes were made of lead.