When the group calls for the second airstrike, their sergeant states that a group of F-111s is headed their way. However, when the aircraft arrive, it is a group of combat helicopters, not F-111 fighter jets.
When "Bones" is looking into the discharge of the machine, his hearing protection is gone. In the shot before we see his eye through the pipe, he has them on his head. When they cut back to the view behind him, they are totally gone.
Bones is offered a promotion to Private First Class (PFC/E3) as an incentive to continue doing his job well. This is incorrect for a number of reasons: Enlisted men in the US Army are not "promoted" until they reach the rank of Sergeant (SGT/E5). Changes in rank from the pay grade of Private (PVT/E1) through Specialist (SPC/E4) are treated as "advancements" since the rank does not convey additional responsibility, only additional pay and seniority. All advancements in rank from E1 to E4 are automatic after a certain amount of time in the Army, whereas promotion to SGT requires additional training (the Primary Leadership Development Course, at the time of filming) and selection by a promotion board. Also, Bones, Jack, Christine, and Fred all graduated from water purification training at the same time, so presumably they have all been in the Army for the same amount of time. As a result, they would all advance to PFC at the same time. The one likely exception would be Fred who mentions that he is a dental student. Dental school is a graduate level school, which means Fred already has a Bachelor's Degree. Anyone who enlists in the US Army who has already earned a Bachelor's Degree would start their enlistment as a SPC (E4). Even if he had not completed his Bachelor's Fred would probably have enough college credit to begin his enlistment as a PFC. Either way, Fred would have very likely been the senior ranking Soldier in the group. Finally, purified water in the Army must meet certain requirements, none of which include taste. US Army water purification units have neither requirement, nor the equipment to improve the taste of their water.
When Bones fires the AT4 near the end of the movie, what comes out is a rocket, exhibited by the smoke trail behind the projectile. The AT4 is a recoilless smoothbore launcher. All propulsion is provided by the charge in the tube, similar to how a normal firearm works. There is no rocket motor on the projectile, and hence no smoke trail.
At a party back home, Bones mentions to his then girlfriend that "he" (his penis) hadn't seen her in 8 weeks, yet he's apparently already fully trained in water purification. After 8 weeks of basic training, an additional 10 weeks of training is required to become a Water Treatment Specialist (the official MOS title).
When Sgt. Stern and his buddies capture Bones, Jack, Christine, and Fred while they are filtering water, they yank Jack and Christine down under the water. The two were in shallow enough water to stand up in about knee length water, but the Sgt. Stern and his posse yank Christine and Jack straight down, when they should have fallen backwards, forward, or to either side. If they were yanked down, they wouldn't go down because they were standing on some sort of surface.