In the very beginning of the movie, before the first voyage, there is a chariot transporting Columbus into a Monastery. The chariot almost runs over some birds at the entrance of the monastery: some chickens and a TURKEY. Turkeys are native to the American Continent, there no were turkeys in Europe before Columbus' travels.
While hunting the white egret on the island, the shooter used an English made matchlock musket with a flared muzzle and a "fishtail" stock. This particular design wasn't in use until the early 17th century.
When explaining navigation to Mendez, about 38 min in, Columbus states "a mistake of one degree, and we will be off 600 leagues." In fact, a mistake of one degree would result in a deviation of 60 nautical miles, about 20 leagues.
The Spaniards all refer to each other by their Spanish names. Other than a few brief references to "Don Cristobal," however, Christopher Columbus is always referred to as such. This is actually the English form of his name, which no one in Europe would have addressed him by. In his native Genoa, his name was Cristoforo Colombo. The Spanish would have addressed him as Cristobal Colon.
When Columbus made landfall on the 1st voyage it was in the Bahamas, probably San Salvador, which looks nothing like in the movie which was probably filmed in Costa Rica or the Dominican Republic according to the filming locations.
In the film, the nobleman Adrián de Moxica cuts the hand of a Native American because he wasn't able to pay taxes in gold to the Spaniards, something which Columbus condemns. In fact, it was Columbus himself who introduced this practice of cutting the hands.
The Nina, Pinta, and Santa Maria are shown starting back for Spain at the end of the first voyage. In fact, the Santa Maria had wrecked by this time; the return voyage would be made only by the Nina and the Pinta.
The film makes reference to three voyages, stating that the second voyage was the one in which Columbus fell out of favor; the epilogue says that Columbus took a third and final voyage to America. Actually, Columbus made four voyages. The second voyage tarnished Columbus's reputation, but it was the third voyage which proved to be his downfall.
When Columbus and his crew first land and enter the jungle, they encounter, among other strange sights, a color morph of an Amazon Tree Boa that is a result of modern selective breeding and a Burmese Python.