(at around 1h 12 mins) When Joe sneaks into Edwina Burke's (Evergreen Headmistress) home while she's talking to Marie, he pulls out a yearbook. He looks into the yearbook and the name says "Adrian Pryce". Then when the shot zooms in, it says "Adrian Doyle Pryce". When Joe and Marie return back to the motel, Marie takes a picture of the yearbook photo where it now returns back to just "Adrian Pryce".
(at around 1h 9 mins) When Marie googles Evergreen Academy, the top result is a link to an article about Edwina Burke from "The Sentinel". When Marie clicks on the link, the article opens in a page from "The Tribune" website.
(at around 1h 30 mins) When Joe and Adrian are walking down a hallway to get Joe's daughter, the hallway is bathed in red lighting. The lighting is no longer red after they open a door and they're seen from another camera angle.
(at around 16 mins) After being imprisoned in 1993, Joe turns on the TV and as he surf the channels a fragment of Xena: A Princesa Guerreira (1995) is seen, but Xena did not start on TV until late 1995. One might think that since this is the first in a series of scenes that montage the passage of the twenty years incarceration, it is not clear how much time has passed between his imprisonment and him watching Xena, but the true crime documentary he watches next gives his daughter's age as not older than four, which means that it can't be 1995 yet.
(at around 1h 18 mins) When reviewing the Evergreen Academy letters, the daughter's last name is spelled incorrectly - Amanda Price instead of Amanda Pryce.
Adrian left a huge amount to chance regarding his plan. There was no guarantee that Joe and Mia would fall in love and they wouldn't have met again had Chucky not phoned her, which itself was coincidental at best.
When Adrian was watching Joe and Maria have a 'moment of passion' with a hidden camera in the motel room how did he know they would rent that room in that motel.
Joe Doucett escapes his imprisonment already having martial arts skills to defend himself, somehow. This actually makes more sense in the South Korean original, as Dae-su Oh would have been exposed to martial arts at some point in his life given his heritage, and it's established that he trained himself to be a fighter while imprisoned. When and how did his American counterpart Joe Doucett learn to fight with martial arts? Nothing in the film implies that he already knew how to or that he learned while imprisoned.