In the Andy Kaufman biopic Man on the Moon (1999), at one point his sister is suspicious of a doctor in a hospital being a paid actor in an orchestrated hoax. She says that he wasn't wearing "doctor shoes". She may or may not have been right within the context of the movie, but what I don't know is:
What would "doctor shoes" be in roughly 1980? Just men's leather dress shoes? A nonslip sole for hospital work? Black? White? Athletic?
What would "doctor shoes" be in roughly 1980?
I have never paid much attention to fashion, so I don't know the different types of men's shoes, but I'll give it a go (at the OP's request. Serves me right.)
Dress "codes" were different based on status. Medical students and interns (first year residents) were the most casual, because they did the scut work, like drawing blood, learning and assisting in messier procedures (ng tube and chest tube placement, etc.) Their shoes were cheap (penny loafers, usually) and in less prestigious hospitals, running shoes made appearances. Surgical residents wore scrubs as well, but better shoes, as they had to wear shoe coverings in the OR so couldn't claim their nice leather shoes would get ruined (not that it didn't happen from time to time.) Other residents dressed as the attending physicians did; it was an unwritten rule.
Men wore nice leather dress shoes, the more expensive, the better. I remember hearing male physicians complimenting and commenting on the shoes of their colleagues, and hearing things like "Italian".
They looked like these shoes:
or these 
Brown or black, and polished, and the highest in the hierarchy (department heads) sometimes wore expensive loafers (?) (pull on shoes).
I never saw a pair of white shoes that I can remember, and no attending ever wore training/running shoes. Some were probably non-slip, as the floors (linoleum) were covered in black "skid marks", what one left on the floor if they dragged their feet when walking.
I haven' thought of that in decades... I was jealous, as my women's shoes had hard soles. Cue slipping!
A person out of the intern stage would not wear casual shoes. The woman in the OP's question would be correct in suspecting a male wearing running shoes was not a bona fide M.D. If tennis shoes were de rigueur, the script itself wouldn't make any sense.
This is based on memory, sorry. But as I was there (a physician in the US, in a decent hospital/hospitals, and a female trying to fit in, I remember what I had to wear.
N.B. I usually avoid commenting on the answers of others in my own, but the photograph in @Valorum's [since edited] answer is a composed (publicity?) shot of a dentist, not a medical doctor. Dentists don't work in the hospital in the US, unless they're maxillofacial surgeons. They can wear what they want and what their patients will let them get away with. The following is a recent photograph of the same doctor as that in the other answer. It is of Elliot Siegel, D.M.D. where DMD stands for Doctor of Medicine in Dentistry. They are not the same as MDs. Nor are television shows always accurate about dress codes.
Edited to Add: Sources!
From Alternative Hospitalist “Uniform” When Hospitalists Were New:
The following is a hospitalist's (a physician who practices only in a hospital) recollection of when scrubs were starting to be acceptable by those outside of the ED in 2003.
I worked for Infinity Healthcare and this occurred at Community Memorial, in Menomonee Falls, Wisc., in 2003....In the course of our formative discussions, we talked about what clothing/uniform would be appropriate. ... in many emergency departments, the practitioners wore scrubs...We arrived at a compromise of sorts—khaki pants and scrub tops in different colors from the emergency department physicians or surgeons.
From Physicians' attitudes about their professional appearance published in Fam Pract Res J. 1989:
Thirty-five residents and 77 staff physicians from three residency programs in Minnesota and Wisconsin completed questionnaires about their attitudes toward various components of the physician's appearance. Most participants showed positive responses to traditional physician attire such as white coat, name tag, shirt and tie, dress pants, skirt or dress, nylons, and dress shoes. Negative responses were associated with casual items such as sandals, clogs, athletic shoes, scrub suits, and blue jeans.
This was in 1989.
From an article in the November 2005 American Journal of Medicine [Re. professional attire and white coats]:
"...Such [professional... and white coats] attire was favored by 76.3% when compared to surgical scrubs (10.2%), business dress (8.8%) and casual dress (4.7%).
From Suits or joggers? A doctor’s dress code published in 2023:
"As a new doc out of residency, I used to wear a tie and shoes that could hold a shine. Now I wear jogger scrubs and sneakers." (Mind you, this is about 40 years after the OP's timeframe! The doc would have to be in their 60's - which is not the case from their photo - to have finished residency in 1983. So think what it was like in 1983...
Finally (maybe), a quote of Dr. Charles Rosen, clinical professor of orthopaedic surgery at the University of California, Irvine, founding director of the UCI Spine Center, School of Medicine, and president of the Association for Medical Ethics:
"In the 1980's when I did residency in NY, it was absolutely forbidden at my hospital... to be seen out of the OR in scrubs. You were to change in and out of and then back in again if you had to leave temporarily. Outside the hospital, residents who would sneak out their scrubs and wear them off hours usually did it to attract women by letting them know they were doctors. Fast forward to the present. Doctors, nurses, along with all sorts of ancillary medical providers like physical, respiratory and occupational therapists will wear scrubs all day long..."
N.B. [never mind; fixed. Sort of.]
And, not to be outdone in the "ridiculous-photographs-as-proof-of-answer" department, here is a photograph of two "hip young doctors" on American TV shows. One is somewhat smartly dressed, the other is dressed very casually, like an orderly.
Note, neither doctor, which represent the extremes of dress (professional/casual) is wearing running shoes. This should provide ample proof that running/training/tennis shoes weren't in the picture.
For those wondering what the heck this last picture is for, see the first answer posted by the user above. This was the photograph which, per the user, is a "picture [is] of a hospital doctor (quite a senior one) wearing scrubs and training shoes." [emphasis mine] N.B. The "hospital doctor (quite a senior one)" is a dentist in a disco modelling specially dyed scrubs.
The script is perhaps a little clearer. It notes that he's wearing old tennis shoes (underlined). Her perception is that a doctor, being an extremely well-paid professional, would not be wearing old anything, let alone a beaten-up pair of training shoes while working in a fancy hospital.
The family nods. The Doctor turns and walks away.
Carol glances down... and notices the Doctor is wearing old tennis shoes. She raises an eyebrow. He leaves.
The shooting script also makes the same note.
Carol watches the doctor with great hostility. His old tennis shoes are grabbing her attention. He leaves, and she frowns.
As to what a doctor should be wearing on their feet, shows like St. Elsewhere depict a growing trend that had apparently started to develop in real hospitals in the 1980s where young, hip doctors would often wear scrubs and training shoes whereas older doctors would stick with the more traditional combination of a suit, white coat and black or brown brogues.
"In the 1980's when I did residency in NY, it was absolutely forbidden at my hospital... to be seen out of the OR in scrubs. You were to change in and out of and then back in again if you had to leave temporarily.
Outside the hospital, residents who would sneak out their scrubs and wear them off hours usually did it to attract women by letting them know they were doctors.
Possibly Carol's perception is skewed by the fact that she's only ever encountered General Practice doctors who have always tended to dress quite smartly in Oxfords.
