I'm no historian but I know for a fact they got Korean and Chinese costumes wrong. For example, the "Chinese" ambassadors who met Hideyoshi were wearing Korean garbs.

One more thing I'd like to point out is that the crucial role Admiral Lee Soon Shin played in the defeat of Japanese forces in the Korean peninsula has been completely left out. I understand that had the producers decided to include the admiral's feats in the show, they would have overshadowed anything that came before or after that point, but I think they had to at least mention a couple of key battles that annihilated the Japanese navy and naval supply line, for the sake of historical accuracy.