The crew is flying a B-24; however, in the closeups of the gunners in action, the top turret is an obsolete "birdcage" type not used in the B-24, and the side gunners are firing from a position that was found only on an early-model B-17.
When PeeWee graduates from gunnery school, his name is called as Williams, R.E. rather than Williams, L. A.
The "Japanese Zeroes" are actually North American AT-6 Texans, popular flying training airplanes used by the Army Air Forces during World War II, Korea, and the early Cold War.
When the B-24 is sent "over there", the map shows that it's headed for the Southwest Pacific Theater, which was composed mostly of tropical islands and a lot of water. The B-24, however, is seen flying over flat, dry land (no water in sight), and when it lands after being shot up, the landscape looks more like Nevada than the Southwest Pacific.