Although the film states it is beginning in Spring of 1941, the calendar in the barber shop does not fit any month in 1941.
When Stella pours drinks for Al and herself, she pours extra for Al. She then picks up the drinks with Al's drink in her right hand, but when she gives the drink to Al, it's from her left hand.
The twenty degree list of the USCGC Periwinkle was just done by tilting the camera - note the tilt of the horizon in the distance.
At the start of the movie, Al is a college senior. It's quite obvious that Andy Griffith was much older than 21/22 (he was 31 at the time of filming).
The women in the movie wear 1950s clothing and hairstyles, when the movie takes places in the early 1940s. The military transport plane in the movie, a Douglas C-54, shows a post-World War II insignia on the fuselage.
In scenes taking place in 1941/42, the jukebox in the bar is a model first manufactured in 1946.
Al wears the rating badge on his left sleeve of a Cook Third Class that was not authorized until June 1944.
At the end of the movie, Woods leaves the bar and walks down the street without his cover (hat). Even though he's distracted by his fiancee', a man who's been in the service more than a week would know that it's military protocol to always wear your cover outdoors.