Continuity mistake: When Sam is making grilled cheese sandwiches with the ironing board and iron, he finishes one sandwich and places it on top of another on the side table. After Joon's explanation of cheese and culture the camera cuts back to Sam placing another finished sandwich on the side table on the same place that he placed the first but there is only one sandwich there where there should be two.
Deliberate mistake: In the scene where Sam is swinging from the hospital window, you see him first from the inside. Now he is obviously being pushed (from a crew member) so it looks like he's moving back and forth smoothly. However, when seen from the outside he couldn't be pushed and so when swinging by himself, he was actually bouncing off the walls. Inside this would have been seen. Also, inside it seems that the sky is clear, though outside there is a tree by the window.
Continuity mistake: When Benny and Joon are riding in the car to Benny's friend's house, Joon looks up at Sam in the tree. This scene is in slow motion, and we can see Benny's hand turning the wheel sharply to the right to turn into the driveway. There is another shot of Sam in the tree, then the shot of Joon is recycled -- Benny's hand is again moving the steering wheel sharply to the right.