It was said that Admiral Yi Sun-sin fights against 330 Japanese ships with only 12 of his own. This is disingenuous statement at best as indeed Japanese navy had 330 ships stationed in Eoranpo, Haenam, but it was 133 ships that passed through Myeongnyang and took part in battle.
Japanese foot soldiers (ashigaru) are depicted somehow correct. It is correct that they used matchlocks (tanegashima) in massive numbers, but they were replacement for the bows (yumi). However, parts of ashigaru used long polearms - pikes (yari) to advance line and protect ashigaru armed with matchlocks. Basically, they fought like European pike and muskets but there wasn't a single ashigaru in the movie with pike unless they took it from Joseon soldiers in a fight.
In the movie, Japanese managed with three ships to surround and naval board Joseon flagship where admiral Yi was. It never happened in reality, and if it happened, Japanese would just slaughter Joseon archers and gunners as there was no infantry on Joseon ships like is depicted in the movie. Joseon ships were twice in size and flagship had many cannons and was full of archers. Those three Japanese ships actually surrounded and tried to naval board captain Ahn Wi's ship but Japanese soldiers never managed to climb on it.
Japanese knights (samurai) are depicted as quick tempered - they pull swords (katanas) out of their scabbards at the slightest offense, and foot soldiers (ashigaru) fought without discipline and formation. One has to wonder how army like that managed to quickly capture most of Joseon in real life? In reality they were highly disciplined and fought in close formations, and not charging like headless chickens.
In one scene, the pirates under Kurushima Michifusa are referred to as being from "Ehime Prefecture", prefectures were not as an administrative unit in Japan until after the Meiji Restoration in the mid 19th century. In the era of the film, that place known as Ehime Prefecture would have been called "Iyo".
Korean navy use maps with modern contour lines 200 years before it was developed by the French engineer J.L. Dupain-Triel.
The Japanese invading force is using Hi-no-maru on their small banners (sashimoto) and flags "only" 270 years early before it became official flag.