Deliberate mistake: When Leonard first writes Teddy's number on his picture, he writes 555-1134. In the rest of the movie, it is written as 555-0134. The handwriting differs as well as the truck seen behind Teddy.
Continuity mistake: In the first close-up Teddy's eyeglasses are upside down, lying near the tile wall, the next wide shot it's upright, further away from the wall, next close-up it's near the tile wall again, lying on the grout just as it's moving in reverse, then in the next wide shot it's further away from the wall once again, lying on the tile, just before it reverses to go back up onto his face. (00:02:15)
Continuity mistake: When Natalie comes home she slams her handbag down on the shelf. As she and Lenny talk and she begins to antagonize him, the handbag changes position within these shots. (01:13:25)
Continuity mistake: The top of the writing desk has different items on it, including a ceramic pot with pens. When Natalie comes home she takes the pens out of the pot and slips them in her handbag. The existence and/or position of the things on the top of the desk change within the previous and following shots of it, including when Leonard searches for a pen. (01:13:25)
Continuity mistake: When Dodd's truck drives behind Lenny's Jag, in the long shot that features one car behind the other, it is clear that Lenny's (driver's side) window is down. When Dodd pulls up beside Lenny, the window is up, as it is when Dodd gets into Lenny's car. (00:52:45)
Continuity mistake: When Teddy is shown getting shot in reverse, at the start of the film, Teddy's right arm position, Leonard's grip on Teddy's clothing, etc., are distinctly different than in the following scene when he is shown again being shot by Leonard. (00:02:30 - 00:06:15)
Continuity mistake: At the diner after Teddy asks, "Where are you staying?" he wipes his mouth with the napkin. The position of the napkin in Teddy's hand differs in the shot facing Leonard and the shot facing Teddy. (00:24:40)
Continuity mistake: While Leonard sits on Natalie's couch rifling through his papers, in the shot facing Leonard, behind him, the two top drawers of the writing desk are open. In the next shot as Natalie comes home only the top drawer is open. (01:13:20)
Revealing mistake: At the 'beginning' when Teddy and Leonard drive up to the abandoned building with the old truck out front, inside the truck Leonard handles a number of .357 revolver calibre bullets that have apparently not been fired, but you can clearly see the indented primers in the base of the bullets, indicating that they are just inert movie props. (00:04:40)
Continuity mistake: While Leonard sits on Natalie's couch looking through his papers, in the shot facing Leonard, behind him, the top two drawers of the writing desk are open. In the next shot as Natalie comes home only the top drawer is open. (01:13:20)
Continuity mistake: While driving, after escaping from Dodd, Leonard pulls out the 'Dodd' note from his pocket and holds it at the steering wheel with both hands. In the close-up of his hands he holds the photos, which face the windshield, in his right hand and the note in his left. However in the shot facing Leonard, he holds the photos, which now face HIM, in both hands and the note is GONE. (00:49:55)
Continuity mistake: After stuffing Dodd into the closet, Leonard holds the note that says, "Dodd white guy 6'2"...919 Booth St.," the note's handwriting is completely different in the wide shots and close-ups. (00:47:45)
Continuity mistake: While Leonard fights with Dodd in the bathroom and after he locks the bolt on the front door, the towel hanging in the bathroom keeps changing position. (00:47:15)
Continuity mistake: When Leonard wakes up in Dodd's motel room, the positions of the pillow under him and the plastic cup on the nightstand differ in the close-up and following wide shot. Then after discovering Dodd in the closet, he goes back to his bed and the pillow, etc., change position again. (00:40:20)
Revealing mistake: At the diner Teddy puts his fingers on Leonard's pulse and Teddy's watch reads 4:45. Teddy jokes that Leonard probably left his key in his room. Leonard goes back to his motel to find his key and asks Burt for the time, to which Burt replies, "A quarter to one," - 12:45. (00:24:25 - 00:26:20)
Continuity mistake: The words behind Teddy's photograph, "Don't believe his lies" are written differently on the same photo three times. First, when Leonard reads it at the abandoned building, second, when he writes it and third when he looks at the photo after seeing a copy of Teddy's license while in room 304. (00:07:00 - 00:13:05)
Continuity mistake: When Leonard is running in the trailer park after having realised Dodd is the one who's chasing him, he makes a chair fall while escaping from Dodd shooting him. However, in the next shot, the chair returns to its place.
Continuity mistake: The window in Dodd's motel room is on the right side from the outside. When Leonard enters, it's on the left side. Christopher Nolan acknowledges this mistake on the DVD commentary and even says that no one's noticed it yet.
Continuity mistake: After Lenny woke up on Natalie's bed and was leaving and Natalie kissed him, her lip's deep red injury disappears and reappears randomly.
Continuity mistake: Leonard sits down at the table in room 304 and starts to pull out from the bag the info that Natalie provided. His keys are positioned differently on the table in the wide shot and close-up. (00:12:45)
Answer: The are no alternative endings for this film, all that is on the third disk is the movie played in chronologial order so you can see how things really panned out.