Here are some comments on North America:
USA: If they go with the planned capital, it winds up in IOTL Washington because, well, its where Washington lives (just across the river) and the North-South split was already emerging as an issue and its just within the South. Path dependency then keeps it there. The center of the US population has for some time been closer to St. Louis (actually its now closer to Springfield), and Chicago is at the center of most transportation networks, but there is no plausible crisis that cold budge it from Washington. Even after a nuke attack by terrorists the place gets rebuilt. You need to engineer a second civil was in the twentieth century, which would probably involve nukes.
No planned capital means that the capital stays in Philadelphia, again because of path dependence. The main problem with Philadelphia is that the slaveholding federal officials had problems keeping their household slaves there once Pennsylvania abolished slavery, but of course that is the entire reason for the provision allowing Congress to create a separate federal district.
Canada: Good comments above, but if the capital stays in Montreal, its a very good POD for a timeline because it means the anglicization of Montreal, with lots of butterfly effects on Quebec.
Somewhat similarly, keep the capitals in Philadelphia/ Montreal/ Melbourne/ Rio de Janeiro instead of moving them to the planned cities, and you have a decent chance of these cities becoming as large and important as New York/ Toronto/ Sydney/ Brasilia.
Mexico: There are two ways to do this. Cortes decides not to rebuild Tenochtitlan, in which case the capital probably winds up in Puebla or maybe Tlaxcala. Or the Aztecs don't become the leading power on the plateau right before the Spanish arrive, in which case the capital could be anywhere on the plateau.
I just don't see alternative capitals for Cuba, or for all those small Central American and Caribbean countries.