When Gutterman is first coming in to land he's flying a A6M "Zero" fighter (actually an AT-6 trainer modified to look like a Zero, this was used in the 1970 movie TORA TORA TORA; much footage from this movie was used in the series.). After landing the aircraft is an D3M "Val" dive bomber (a BT-13 trainer modified to look like a Val, again from TORA TORA TORA.). When taxiing up to stop it's now a B5M "Kate" torpedo bomber (another BT-13 modified for TORA TORA TORA).
There never was a US invasion of Christmas Island.
Through out the series when the Black Sheep are landing on an aircraft carrier they show it an angled flight deck. Carriers did not appear until the mid 1950's. CV-61 was shown the USS Ranger commissioned in 1957.
The ship shown docked in the Navy shipyard is the "Hawaiian Legislator", which was actually built in 1946, one year after WWII ended.
A subtitle uses "there" instead of "they're".
The "UNIVERSAL NEWSREEL" at the beginning shows a Copyright date of MCMXXXIX, which is 1939. The U.S. didn't enter WW II until the attack on Pearl Harbor, which was in December 1941.