1) Cinco de Mayo. It's ubiquitous in the States. If one's not careful, though, he might think the holiday celebrates Mexico's independence from Spain (1810). Nay. It celebrates Mexico's defeat of France when the latter sought debt collection, ca. 1862. However, after this battle in Puebla (state just north of Oaxaca), the French recouped and routed the Mexicans... then occupied central Mexico for some time.
2) The "X" in so many words. You'll be hard-pressed to come across so many of these letters outside of Mexican Spanish. Our professor here told us that, later in the 1800s, starting with "Mejico," the country's leadership changed "J" for "X" in many words as a way of flipping the bird to the Spanish; to establish an identity away from the conquitadores.
Repeat these two histories at your next dinner party and you're sure to impress all attentive spectators.