Deliberate mistake: In the parking lot at the horse track, the old cars are so huge, they don't fit properly in the tiny modern spaces. They are hanging over the backs of the spaces so badly that the drivers would only have about two feet to try and get their enormous cars out of the spaces.
Continuity mistake: When Slevin is in Nick's apartment the second time, eating the sandwich, the way he holds it changes between shots.
Continuity mistake: 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.
Continuity mistake: After sleeping with Lucy Lu, Slevin is standing over her; her hair is spread out all over the pillow and then is suddenly neatly tucked behind her head.
Deliberate mistake: Look closely at the horse track parking lot. To fit more of the cool period cars in the shot, the director has the next row of cars parked in what should be the driving area between rows.
Continuity mistake: When Lindsey is telling Slevin about taking the elevator with "Smith", we see her taking a picture of Smith, while pretending to have a phonecall. She makes a picture of Smith full in his face. When she's showing Slevin the picture she made, it's of the side of Smith's face.
Continuity mistake: Lucy is sitting on the counter, drinking a bottle of water as she talks to Josh. Most of the time the Kirkland label is facing out, but just when she says, "You're f***ed" the UPC code is facing out.
Continuity mistake: In minute 5, when Nick Fisher raises his hand, his watch wasn't touching his sleeve and the time on it was 4:30 and 47 seconds. In minute 105, when the scenes were repeated, the watch is partly under his sleeve and the time is 4:32 and 40 seconds. (00:05:00 - 01:05:15)
Continuity mistake: When Slevin finishes shaving he wipes most of the shaving cream off his face and stares at himself in the mirror. There is still some shaving cream left on the underside of his chin and neck though. When there is a knock at the door the shot changes and the shaving cream has vanished.
Continuity mistake: When Bruce Willis is playing chess with Morgan Freeman, he is primarily playing with his left hand. At one point, Bruce has a chess piece in his hand, they quickly cut to Morgan, and when they cut back to Bruce, the piece is in his right hand.
Factual error: In the parking lot of the race track, as the camera zooms out you can see a new Ford Thunderbird. This is impossible, as the scene takes place in 1979.
Revealing mistake: When Lindsey runs to answer her phone after she asks Slevin to explain why he was still wearing a towel, you can see the tattoo on Josh Hartnett's left shoulder blade coming through the makeup.
Answer: I've considered 2 possibilities. One being the answer given about his cover, but I think he may have actually had it. When Goodcat is pointing a gun in his face as a child, he doesn't look scared in the least. The death of his parents "killed him" giving him the condition. Later proof is when he tells the Boss "You can only kill me once."