There are two main “enduring vulnerabilities” that come with being the world’s only superpower.
First, there are vulnerabilities in terms of the cost of being a superpower. These include costs in both money and human life. Because the United States has been the world’s only superpower (and, before that, the superpower that led the free world), it has been responsible for bearing the costs of keeping order. The US had to pay to help European countries and Japan rebuild after WWII, only to have those countries start to compete with the US economically. The US had to send soldiers to die in places from Vietnam to Iraq to Afghanistan. These things do not happen to nearly the same degree to countries that are not superpowers.
Second, there is the vulnerability that comes with being a target. Because the US is the world’s only superpower, it is the country that all dissatisfied people have a grudge against. It was the US that was attacked by Al-Qaeda because it is the US that is a superpower. It is the US that Iran hates most because it is the US that tries to keep order in the world.
Because the US is the world’s only superpower, it is a target for everyone and it has to spend money and lives trying to keep the world safe and stable.