Deliberate mistake: In the Extended Cut, when Fujiwara arrives at the mansion, he asks Sook-Hee "So are you carrying out your duties faithfully", then Hideko says "Thank you for introducing her." Later on, when a scene also included in the Extended Cut shows the same scene play a second time, after Fujiwara says "So are you carrying out your duties faithfully" to Sook-Hee, the two share some strange looks that weren't shown the first time. This was done because the moment between them was a scene that was included in the Theatrical Cut, the first time his arrival was shown, but was altered in the Extended Cut to not show this, because their true reason for being at the mansion was not revealed until later and including this brief moment would have given the twist away too early, whereas the Theatrical Cut included a scene that established their intentions much earlier on. The Extended Cut included these brief glances when shown the second time, but still makes for an inconsistency between the two scenes. (00:23:35 - 01:52:00)
Deliberate mistake: The movie is set in the late 50s, but Howard Hughes is dealing with his plane crash and the senate hearing about the H-4 Hercules prototype. Those are events from over a decade earlier. However, it should be noted that the initial disclaimer of the movie is "Names and dates have been changed."