Pappy and Hooper hop out of their floating Japanese plane, nonchalantly stand on the wing root, and point and wave at the Black Sheep flying overhead. Planes don't float.
The Universal Newsreel copyright at the episode's beginning is 1939 (MCMXXXIX). This date is incorrect based upon the time frame of the series. VMF-214 under Major Boyington started flying in 1943.
The rescue seaplane that comes to pick up Boyington and Hooper has US insignia with red stripes over the white bars on either side of the white star. The red stripes were not added until 1947, two years after the end of World War II.
Near the end, a drunken Pappy Is returned to his unit and surrounded by members of the 214. He sees his dog, Meatball, and calls to him. Meatball walks to him and then past him toward a partially blocked off person wearing blue jeans in the background. That was probably the animal trainer. Everyone else in the shot is in uniform.