An enlisted man walks into the Colonel's office wearing Private First Class insignia of one chevron with one rocker. This insignia was not used until 1968, well past the time period that the film was set in.
Near the end of the film, Vince Johnson (Powers Boothe) is watching an in-color news broadcast on a color television. Color television sets weren't widely in use until the mid-60's, and news broadcasts were virtually all in black-and-white until that time.
While the film deserves credit for showing the US Army using Bell H-13 Sioux helicopters in 1963, and a UH-1 Huey in high visibility, full color markings- both of which are correct for the era- one scene shows a Bell OH-58 Kiowa flying over an atomic test sight in 1963.
Nice try, but the Army didn't start using this chopper until the spring of 1969.