As a Korean-American, who has not watched the two episodes of JE that were aired, I just want to provide a little more information.
As to King Taejong and King Sejong, they are historical figures beloved by Koreans, unlike Cheoljong (in Mr. Queen) who was thought to have been an incompetent ruler.
As to the Chinese influence, it was a very bad timing because the China-Korea cultural feud had been intensifying since the Northeast Project.
From what I read in Korean newspapers, Shin Hye Sun lost one advertisement.
My two cents, for those of you who dismiss the Koreans’ outrage over distortion of facts, is that there is a fine line between creative liberty and distortion of facts. Also, many K-drama viewers learn about Korea through what they watch on the screen. I have personally been asked “I saw on a K-drama…, is that true?”