(at around 23 mins) Lindsey's socks when she leaves the room after getting the sugar are white. When she comes back to the room, her socks change from white to red.
(at around 1h 9 mins) When Slevin walks through a hallway to The Fairy's room, there is a part of his hair on top of his head that changes from being flat on his head to standing up various times.
(at around 37 mins) When Slevin is eating the first sandwich he eats in the movie, it changes from being half eaten to having only one bite taken out of it.
(at around 1h 1 min) When Slevin and Lindsay are walking back from their date and talking about picking up a pigtail, there is an extra behind them that disappears and reappears several times.
(at around 37 mins) Also with the sandwich, the eaten bites rotate from being the bottom corner to the top corner on multiple occasions.
(at around 1h 1 mins) When discussing Bond villains, Slevin refers to Ernst Stavros Blofeld. The character's middle name is in fact Stavro, without the second S.
(at around 1 min) At the beginning of the movie, when Slim Hopkins gets shot in front of the door of his car, the window's glass is already broken before the bullet goes through him into it.
(at around 11 mins) Towards the beginning of the film at the horse track, they show a horse fall during a race in 1979. In one of the scenes, you can see a new John Deere tractor in the upper left hand corner of the screen.
(at around 4 mins) During the opening credits when Nick is walking towards the camera to sit down, you can see the reflection of the camera man moving around in the back of the front left blue chair.
(at around 22 mins) While Sleven and Lindsey are talking about what happened to Nick, Lindsey picks up the apartment phone and presses the spring button twice and connects to the last caller. That action would only result in a dial tone.