Why, in your words, is he an embarrassment to the US and a joke to the rest of the world?
Although his 'base' thinks his crassness and public insults are just what we need in a president because "he tells it like it is", many others disagree.
One example of him being a joke is when he bragged about his accomplishments to world leaders at the United Nations General Assembly in New York. Or maybe they simply thought he was joking when they all laughed. I'll give him some credit for laughing at himself during this event.
He lies, he insults people, often making irrelevant comments about their appearance, intelligence and their personal lives. Some may think that his juvenile behavior is cool, while others believe his lack or decorum is embarrassing.
It's impolite to comment about someone's appearance, so I won't. However, it is often the subject of jokes.