@noobchicken America's mistake was allowing journalists to record and release the footage to the US.
Truth was, Vietcong ceased to be an operational entity after the Tet Offensive and had to be absorbed into the NVA. The NVA itself was on the verge of collapsing. Another few more months, and the war would've been won for South Vietnam.
However, public perception drives everything, and the war was deeply unpopular at the homefront cause of the images and recordings making it back.
Though if you really wanna trace it all the way back, the mistake was in thinking there was a need to fight communism. How many communist countries collapsed on their own, or adopted capitalist reforms and policies?