In Japan, before entering a communal bath, one is required to shower first so as to be clean when entering the water. When Gilbert and Mitsuo walk up to the entrance door for the bath, both are completely dry. Public baths in Japan are nude, and Gilbert is shown to be wearing a pair of knee-length swim trunks under his robe, while Mitsui is correctly naked.
Gilbert is flown to the Korean front lines in a Helicopter marked U.S. Air Force. While the USAF did operate the Bell 47, they would never be used in a role like this. Gilbert would have been brought up to the front using a US Army Helicopter instead.
All of the cars, trucks, and aircraft at what is supposed to be Tokyo International Airport are Ameican made. While there may have been a moderately heavy presence of US aircraft there, there were very few American-made automobiles in Japan at that time.
When the USAF C-54 lands and taxis into what is marked "Tokyo International Airport", across the field, the exact same aircraft parked in exactly the same place can be seen parked at the airport that the USO C-54 was leaving from in the US.
When Gilbert Wooley arrives at the airport in the taxi, his rabbit, Harry, is sitting on the roof resting up on the luggage rack. The silver aluminum brace used to hold Harry up can be seen wrapped around him as he approaches. When the cab pulls away with Harry still on the roof, not only is the brace visible, but the base of the brace can be seen to be riveted to the top of the cab, painted the same color to match the taxi itself.
When Gilbert is being flown to the Korean front lines in the Bell 47 Helicopter, the aircraft has no registration number. It is just painted olive drab and says U.S Air Force on the side in front of the tail rotor.