The wall calendar Eliza uses is from the fall of 1962, yet the newsreels shown on television and the narrator's reference to "the last days of a fair Prince's reign" make it clear it is early May 1963.
The exterior of the lab was filmed at the University of Toronto Scarborough Campus, built 1963-1965 with Brutalist architecture style, which was new to the US and Canada, but the interior looks old and worn.
Early in the movie, Strickland states he brought the creature back from the Amazon, where the natives worshiped it like a god. Later, as Elisa and Giles are attempting to take the creature from the lab, Hoffstetler, while helping them, says they need to add salt to his water along with the water conditioning chemicals he gives them in a box. However, the Amazon is a freshwater river, and if the creature was from from there, it would not be used to nor need a saltwater environment.
When Strickland (Shannon) drives home from the dealer's with a new Cadillac, the car has a regulation Maryland license plate. A temporary cardboard plate would have been issued for the first couple of weeks of ownership.
As the Strickland family watches "Dobie Gillis" on TV, the son asks if they can watch "Bonanza". The two TV series were never on opposite each other: "Bonanza" was on Saturday or Sunday (depending on the year) and "Dobie Gillis" was on Tuesday nights.
A 5 star general would not exist in 1962. The last 5 star general was Omar Bradley in 1950 and would have been long since retired. The U.S. military historically has only used this rank during times of war in order to achieve parity with or even outrank allied commanders from other nations under their control in combat.
The general's ribbon bar is upside down. The Silver Star and Distinguished Service Medal were his highest honors, and should be on the top row, not the bottom. His WW2 Victory Medal is much lower in precedence and should be on a lower row, not the top.
At around 17:50, security is leaving the men's room and you can hear a door latch. when the door opens and closes. The door has a handle, not a knob. Therefore you would only hear a thump as the door hit the door jamb closing.
A WWII era sign is shown "Loose lips sink ships" that would unlikely be still shown in the early 60's. It would make sense for a government institution to still be using surplus posters from the war, as they are still trying to discourage the sharing of secret information.
After Dr. Hoffstetler is shot in the mouth, a gaping hole is left in his cheek. We then see him down on the ground, with his mouth open and a bright floodlight shining on his face, and yet no light shows through the hole at all.