When General Moore tells Greg who he is, Greg is skeptical of his identity, however, in later episodes they are portrayed as long standing friends, even knowing each other in Washington D.C.
In the first dog fight when Boyington goes up against two Japanese Zeros, there are several brief cockpit views where the bandage on his left cheek moves to his right cheek, and then back again to his left cheek.
In the dogfight over the mountains, the fuselage of the second Zero is white, then dark, then white and finally dark as it burns in.
Fleet Admiral Chester Nimitz' son Chester Nimitz, Jr. was a navy officer in the Pacific Theater (winning a Navy Cross as a submarine commander). However, his nickname was "Chet," not "Teddy" as both Boyington and Nimitz suggest during their phone conversation.
Boyington is depicted as leaving the Flying Tigers a week after Pearl Harbor. He actually left in the summer of 1942.
Colonel Mathys, an army officer assigns Boyington to Esprito Marcos. Army officers would not be in charge of personnel assignments for US Marine Corps officers during World War II.
Although the show says, and the real Boyington claimed to have shot down 6 planes as a Flying Tiger in one day, records did not support it. It's entirely possible that he may have as records were destroyed in attacks, but it was never officially recognized.
They have Admiral Nimitz at an office in the Pentagon, the only trouble was he was at Pearl Harbor during World War 2.
Near the beginning, when Boyington shoots down the second Japanese fighter, black smoke begins to pour out of the left side of the aircraft. Instead of the smoke trailing behind the plane as it moves forward, the smoke hangs in a cloud next to the plane indicating that the aircraft is sitting still in midair, which is an impossibility.
Boyington is lying on his cot reading the files on three pilots (Gutterman, Bragg and Wiley). With the exception of their names and ranks, all three files are exactly the same, word for word.
Pappy calls Admiral Nimitz during a conference in a clearly complete Pentagon immediately following Pearl Harbour. The ground breaking took place only two months previously, and entered into use two years later.
As 2 Zeros are jumping Pappy as he is on way to Pacific you can clearly see the contrails of a passenger jet in the background.