The animated segment at the beginning of the film is based on Private Snafu, a series of adult-oriented instructional shorts meant to educate enlisted personnel on army discretion, hygiene, combat readiness and daily life. They were produced between 1943 and 1945, and given that they were not meant to be public, were free from censorship restrictions. The title character, parodied in the film, comes from the military acronym "Situation Normal, All Fucked Up".
During WWII the Women Airforce Service Pilots -- WASP for short, was created by the USAAF. These lady pilots, more than 1,100 flew military aircraft. Single to multi-engine aircraft. From non-combat like transports and spotters, to fighters and bombers including the B-17, B-26, and B-29 bombers. Henry "Hap" Arnold said he wasn't sure "whether a slip of a girl could fight the controls of a B-17 in heavy weather." Later he ate crow and admitted how wrong he really was when he said "Now in 1944, it is on the record that women can fly as well as any man!"
Whilst it may be claimed to be incorrect that the female aviator is a Captain in the U.S. Army Air Corps, female pilots were used to ferry finished planes from the assembling factories to the air bases from which they would fly operationally. In Britain, female pilots would single-handedly deliver Lancaster bombers to the RAF Air Bases, sometimes flying two or three a day totally alone and eating their meals as they flew. It's not an unusual or inaccurate concept to have an American pilot doing the same, even if her credentials are inaccurate.
The original screenplay penned by Max Landis was heavily rewritten during pre-production by director Roseanne Liang due to sexual harassment allegations made against Landis at the time. Liang and lead star Chloë Grace Moretz say Landis was completely distanced from the production and that his screenplay was rewritten several times before filming began. However, after watching the film Landis claims that about 90-95% of the script is still his.
In the 1943 Bugs Bunny cartoon "Falling Hare", Bugs tries to prevent a gremlin from crashing or otherwise destroying a B-24 Army Air Force bomber. The cartoon is a popularization of military concerns about "gremlins", or unrecognized or undiscovered flaws, causing problems in military equipment during the war.