This is treated as the first time Doctor Dudley and Herman Munster have met. But in a prior episode, Rock-a-Bye Munster (1964), Herman visits this same doctor's home and he and the doctor mention this trip to the office for his physical and the doctor fainting at the sight of Herman. This may be due to a difference in production order and airing order.
When Herman visits the doctor, the backs of his hands and fingers are covered in hair that was not there in the previous or following scenes. The hair appears and disappears throughout the episode.
When Dr. Dudley is asking Herman about his medical history, Herman mentions that he once had the Black Plague. The Black Plague ended in 1353, while Herman was completed around 1850.
At 12 minutes in, the Nurse (Caryl Rowe) knocks on the door to return the Doctor's (Paul Lynde's) glasses. The Nurse flubs her line, mispronouncing the word "glasses." Obviously thinking this blooper would necessitate a retake, the Nurse laughs and waves at Lynde before turning awkwardly away. Actually quite funny to watch her reaction.
Lily tells Herman that she doesn't want him to go to his Army unit's reunion because he'll have to be away overnight and they haven't been separated in over 100 years. Even if Herman never left the country while in the Army, he would still have been away from her during basic training. But it appears that he did leave the country, and was stationed at Fort Benning and then overseas, where the enemy ran from him when he got out of the foxhole.
When Herman goes for his physical his hands are visibly hairy and the Doctor makes a comment about his hands telling Herman he has to leave his doggie outside. In all other episodes Herman's hands are not hairy.