Continuity mistake: When Homer is threatening to boot the Prime Minister, he is holding him still with his left arm. When the shot goes to behind Homer, he has his right arm on the Prime Minister's shoulder. When the shot cuts back to a direct view of Homer, his right arm isn't touching the PM.
Factual error: The Suburb of Wooloomooloo where the chase starts is in Sydney, and the Simpson family are chased all the way to the American Embassy which is in Canberra, a distance of at least 150 kilometres. That's some impressive running, especially for Homer.