Leonard Shelby: Facts, not memories. That's how you investigate. I know, it's what I used to do.
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Continuity: 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: 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.
Visible crew/equipment: Teddy, Leonard and Jimmy leave Jimmy's motel room and Leonard tells Teddy, "Take your own car." In the next shot as Teddy reaches for his door, a crew member, plus another one under his arm/elbow, are very clearly visible in the door mirror. Then as Teddy closes the door a crew member's face is seen on the left, in that mirror.
Continuity: At the beginning of the movie, Leonard looks outside his window and sees room 304 (which will be given later to him on top of his current room) - it is on the same floor he is currently on. Still, when he learns from the clerk that he has been ripped off, we see them both coming out of room 21, which probably is room 221 with the first 2 missing, because it's next to the reception, itself located on the second floor (we know that because from room 304, Leonard only needs to go down one flight of stairs to reach it). Both his rooms, 304 and 221, could not possibly have been on the same floor.
Deliberate "mistake": In the Sammy/Lenny shot in the Institution, before the switch the orderly on the left heads toward the medical files with his arm outstretched and the nurse walks behind Sammy. Just as the person passes the camera the film jerks and the two men at the table, visible on the left, have a shaking motion. After the switch, the orderly and the nurse are both further back.
Continuity: When Leonard is looking at the note that reads, "Dodd white guy...get rid of him for Natalie..." in the wide shots as Leonard holds just the note, many photos are lying on the bed under his hands. Yet in the next close-up, the suit is spread out right under his hands as he holds the note with a single photo, that he soon drops, and no other photos are seen.