When Dixie arrives in England in December of 1942, there is a P-51 Mustang on the ramp. This airplane was not in service in December 1942. Also this airplane has the black and white identification stripes not used until June 6, 1944.
During the WW2 North African performance sequence, the military
photographer is using a Speed Graphic Pacemaker, which wasn't
made until 1947. Conversely, in the party sequence in Japan (1950), a military photographer is using a PH-47 Anniversary model Speed Graphic, the WW2 military camera of choice.
In the film during a World War II sequence Bette Midler sings "Come Rain or Come Shine" which was not written until after the war and wasn't introduced until 1946.
During a skit on an early Fifties TV variety show, Dixie makes an off-handed joke about group sex that would have triggered a major scandal had it really been broadcast during that era.