Yossarian's new tent-mate introduces himself as "Lieutenant Newman," however the rank insignia on his uniform is the insignia of a sergeant.
During the awards ceremony some of the airmen receiving the awards are at the position of "parade rest" they should be at the position of "attention." When receiving his award Yossarian is saluted by General Dreedle, who drops his salute before Yossarian returns it, and is then saluted by Yossarian. Yossarian should have saluted the general first, held his salute until the general returned it, and dropped his salute after the general dropped his.
Flak explosions appear to move towards the camera even when the camera is stationary and the planes are flying away. Actually the camera is still chasing the planes, albeit at a slower speed.
Throughout the series General Sheisskopf is obsessed with drilling his troops be the best marching unit in parades that he regularly schedules. The troops marching in the parade are obviously out of step and marching poorly, so either Sheisskopf failed, or the production didn't have enough people familiar with military drill and ceremony to give the impression that he succeeded.
The new tail-gunner has no parachute.
After all the in-flight carry-on, the clasp of Yoyo's dog-tags chain is perfectly aligned at the back of his neck when he walks away from the plane.
It could just be coincidence. In the last scene when he embraces the new Lieutenant, it is at the back, but it is not centered.
In the post hospital Yossarian's blood pressure is checked and you hear the familiar, ripping sound of the Velcro hook and loop closure. However, while Georges de Mestral conceived the idea in 1941, it would be another 8 years of research to get it to work and another 6 years to bring it to market.