How has America's ability to act worldwide been affected by the fact that some of the most dire claims made in support of the Vietnam War ultimately proved wrong?
It is hard to answer this in any objective way because we cannot know exactly how the incorrect claims (as opposed to other factors) affected America's ability to act.
America's ability to act has been constrained to some extent (one might argue) because other countries will be less likely to believe in claims that the US makes. For example, we can argue that countries are less willing to heed American claims about the dangers posed by Iran's nuclear program because the US was so wrong about the "domino effect." However, it is difficult to be absolutely sure that this sort of problem truly came about because of the Vietnam War.