Basically, Mexicos is eliminated almost all the time, and the games that "go well" make the country a secondary power at best. Looking at how players act in game confirms this; only once has Mexico ended at 20+ centers (they got a 3rd place in a draw at 26 centers. 37 is solo), and that game had USA in CD.
In the early game the main problem is that Mexico and the US both has as priority nr 1 to deal with the other. If one of them tries to go the other direction, they will be stabbed, and very few games do not have a US-Mexican war by 1902. The design is made to try to promote Mexico-Colombian, Mexico, Argentinaian, and US-Colombian wars, but this rarely happens in the first years. Mexico-Colombia fights sometimes, but Colombia is a pain in the ass to gain on as Mexico. Colombia is also the best preforming power in the Americas, which might be conntected to Mexico's poor preformance and vice versa.
Mid-game Mexico faces the problem that the centers quickly run out. Again, the most likely situation is that USA has been taken, since USA is the first priority and Colombia such a pain to take over. This puts Mexico in a situation were oceans and tricky lines must be crossed, but without the size usually connected with this as North America does not have many centers.
Any late-game issues for Mexico are unknown since Mexico do not tend to get that far. At any rate, late-game situations do not tend to be quite as country specific.