Loretta Swit's fingernails are over an inch long. No nurse, especially a head nurse, would have fingernails that long.
During Colonel Potter's physical, Hawkeye removes a blood pressure cuff that has Velcro. The first patent for Velcro wasn't granted until 1955 in Switzerland. It wasn't even mentioned in the media until 1958. It's first noted use was by NASA; and it didn't come into broad use until the 70's when the original patent expired.