The doctor at the radiography station says he's overworked and checks his pulse, but he pressed his thumb to his wrist. Anyone with medical training knows that because there's also a pulse point in the thumb that it cannot be done this way. Feeling for a pulse is always done with the forefinger.
Bugs' x-ray shows bones outlining his ears. Rabbits, like humans, have ears made of cartilage, which does not show on x-rays.
The chickens are shown all dressed up in formal attire.
One chicken is shown eating food off the floor but there is no food on the floor.
The crescent moon is shown with stars visible directly behind it even though that would not be possible.
The same men who are waiting with Bugs Bunny for their examination are also the exact same men who are shown in line with Bugs Bunny holding their Army gear.
Bugs can read everything on the eye chart, including the microscopic writing at the bottom, but didn't realize the envelope said "B. BONNY" and not "B. BUNNY".