Continuity mistake: In the scene in which Leonard writes on the back of his picture of Teddy, "He is the one. Kill him," we see a shot of Leonard placing the picture on top of his tan jacket on the bed as he goes to write on it. Then, it goes to a close-up of the picture in which the jacket has disappeared and the picture is lying directly on the blue bedspread. It actually happens twice within that same scene.
Continuity mistake: After entering room 304, Leonard steps on the bed to put the 4 photos back up on his paper on the wall. In the 1st close-up he puts the Discount Inn and the 2nd close-up he puts up Natalie. Then in a wide shot of Leonard looking at the paper, visible at the top of the paper, in the center, is the photo of Natalie and on it's right is the photo of Teddy, already up. In the next shot, the 3rd close-up, he puts up his car. However in the next wide shot ALL three photos that he just put up in the close-ups are GONE. Then in the 4th close-up he puts up Teddy's photo, which was up in the first wide shot.
Trivia: In the scene where Lenny is on the phone describing how Sammy Jenkis ends up in a home due to the death of his wife, it shows Sammy sitting in a chair looking towards the camera. Sammy is temporarily blocked from our view by someone walking in front of him. As the person passes by, it is not Sammy that re-appears, but Lenny. To see it well, you will have to use the frame-by-frame mode. There are about 5 visible frames of Lenny in the home, and then it cuts back to him inside the motel room talking on the phone again.
Leonard Shelby: I have to believe in a world outside my own mind. I have to believe that my actions still have meaning, even if I can't remember them. I have to believe that when my eyes are closed, the world's still there. Do I believe the world's still there? Is it still out there?. Yeah. We all need mirrors to remind ourselves who we are. I'm no different.
Question: I still don't understand why Leonard switches clothes with Jimmy and steals his car after he kills him. "I'd rather be mistaken for a dead guy than a killer." That makes absolutely no sense. Driving around in Jimmy's car and wearing his suit would make him the prime suspect in the investigation. He was much safer when he was just an anonymous guy driving around in a pickup truck.