America’s ability to act in the world has not been seriously curtailed by the Vietnam War. The simple fact that the US was wrong once does not imply that the US will always be wrong (or will always be perceived to be wrong) when it says that there is a danger.
It is true that there are countries that are unwilling to follow the United States’ lead in foreign affairs. We were, for example, unable to get a large coalition together to overthrow Saddam Hussein in 2003. However, it is in no way clear that this was because of the mistakes of Vietnam. Instead, it seems that countries that are unwilling to back the US are unwilling for other reasons. The Arabs, for example, were unwilling for reasons having to do with their own internal politics. The Soviets and Chinese are reluctant to side with the US on Syria (for another example) because they see themselves as rivals to the US for power and leadership in the world.
Thus, though plenty of countries resist the US on international issues, it is not because of mistakes that may have been made in the Vietnam Era.