Actually, if you consider that the false death date is given in a time line presented in the spirit world, the date is not wrong, but is the real date from another time line, the original one, the actual death date being altered by his actions. So being a fantasy film, is no anachronism.
The scene with the young Leo and the old Leo told us that, as an inside thought, he was born in1452 at Vinci and died in 1522 at Nanterre - France. Maybe this is because the young one was not able to read in crystal balls but in fact the real Leonardo died in 1519 at Château d' Amboise - France.