When Dodd first comes after Leonard and chases him, his red SUV blocks in Leonard's Jaguar from behind. However, in the next chronological scene (when Leonard gets back to his car and drives away), Dodd's SUV is no longer blocking him in.
When Natalie kisses Leonard goodbye, her lips are not cut, though they are before and after.
When Leonard burns Catherine's hairbrush in the fire, you can
see that Catherine's book is also burning next to it before Leonard has put it into the fire.
In the black/white parts Leonard is staying in room 21 (as seen on the key). In one of the shots he looks out the window and we see the door to room 304. In the clip it is at the same height as the room Leonard is looking out of, but when he moves into that room he has to go down the stairs to get to the reception and in doing so passes room 21.
Natalie's photograph which has some cancellations and then written something else, the cancellation is very shown as if down by a black marker. However when Leonard is shown making the cancellation on Natalie's photograph it is done using a ball pen and the cancellation is untidy compared to the prior black marker cancellation.
Possibly deliberate: A shot shows Teddy's Driver License with its expiry date clearly visible: 02/29/01. But the year 2001 is no leap year, thus there is no 29th day in February.
The vial of insulin used by Sammy has the lettering "C-II" on the label, indicating that a medication is a controlled substance (schedule II). C-II medications are those with high abuse potential and include narcotics like morphine and fentanyl. Insulin is not a controlled substance, much less a C-II, and would not have this designation.
The Jaguar XK8 has antilock brakes and would not have managed the entertainingly screeching skid as it stopped outside the tattoo parlor. Only the rear wheels are locked and clearly the handbrake was used to make an amusing noise. No matter how it was achieved, it was not a natural stop and there is no evidence to suggest that Leonard is a stunt driver who might habitually stop like that.
Fact number 5 is tattooed by Lenny himself with a very fine needle so it would take an enormous amount of time and a steady and skilled hand to write thick letters as shown.
When Natalie shows Leonard the picture of herself with Jimmy, she is smiling (in addition to Jimmy having a mustache). Later, when he gets out of bed and views it again, she is no longer smiling, and Jimmy's mustache is gone. Finally, in the close-up of Leonard writing the note on the back of the Polaroid he took of her, the picture has reverted to its original state. This is probably deliberate to make us feel we have Leonard's condition.
Sammy Jankis is reported as having "possible damage in the hippocampus, nothing conclusive" but the CT scan of his brain shown at the time is grossly abnormal. It shows a large left sided subdural haematoma (bleed) with significant mass effect. It is very likely that a patient with such a scan would be seriously unwell. However, since Sammy is a fabrication of Leonard's memory, it is highly likely that this brain scan is in fact a scan of his own brain, fitting the description of bleeding.
...or not - your call. Since the movie is about memory and its fragility/unreliability, it is eminently possible that all supposed continuity errors are deliberate. However, given the structural complexity of this movie, and bearing in mind the number of errors which manage to find their way into even the simplest linear narrative, it is equally possible that they are genuine errors and so they are reported here for your consideration.
Leonard is able to remember that he has a problem with his memory because he has conditioned himself to look at his "Remember Sammy Jankis" tattoo. Similarly he has conditioned himself to check his pockets for Polaroids to remind himself of other essential day-to-day facts. Alternatively, it could be because Leonard has Korsakov's syndrome, sometimes caused by acute trauma. In some cases the patient knows that they have the disorder. Arguments have been presented both for and against this but, in the end, it's the reality that the movie presents us with and so, for 113 minutes at least, it's true.
Natalie's handwriting is different in each of its appearances. The writing on the Ferdy's Bar coaster switches between print and cursive, and the invitation to the City Grill is in another kind of print. However, this could be another demonstration of the instability of Leonard's memory.
When Leonard discovers the bullets in the pickup, the primers are obviously used and would not fire.
When Teddy asks Leonard to roll up his car window near the beginning of the film, the top of the intact window is briefly visible, pushing the loose shards of glass, before retracting.
Teddy's head is pulsating when lying on the floor after having being shot.
When Natalie asks Leonard to give back her shirt that he's mistaken as his own, Leonard's wearing a man's shirt. The location of the buttonholes give it away. Leonard would have struggled doing up the buttons on a ladies shirt.
In the close-up shot of Natalie's head on Lenny's torso, you can hear Lenny talk with the same voice whether he is breathing in or out.
When Leonard and Teddy are in the diner, Teddy says "What about John G.? You think he's still here?" When the scene cuts back to Leonard, the line "You think he's still here?" is heard, but Teddy's mouth isn't moving.
When Dodd pulls his red vehicle into view after Leonard turns
off the road to see what he was harassing him about, the camera crew is reflected on the side as the truck moves from the right side of the frame to the left.
When Leonard is sitting in his pick-up writing down Teddy's license number, he writes "FACT 6" without checking how many other facts there are first.
Leonard goes to the Discount Inn, and the manager takes him to room 303; when Leonard realizes that it is not his room and the manager admits to also renting him room 304 because business was slow, Leonard calls the manager Burt. In that particular entire sequence, Burt has on no name tag, nor does he mention his name to Leonard.
During the confrontation between Leonard and Teddy after Leonard has killed Jimmy, Leonard mentions the $200,000 in Jimmy's car. However, at this point he has already forgotten about killing Jimmy, so he should also have forgotten about the money as Teddy doesn't mention it.
Leonard has several tattoos on his chest and arms that he would never be able to read clearly himself; they are not reversed so that he could read them while looking at himself in a mirror, nor are they upside down so that he could read them by looking down at his body. The only person who could read them without difficulty would be someone who was staring directly at Leonard, making these tattoos useless to Leonard himself.
While the fact that Leonard wrote "do not trust her" in a different style of writing, so that he knows to be suspicious of it, is supposed to be a detail deliberately added, Leonard also followed notes written by Natalie more than once, even before he had a Polaroid of her, or any reason to trust her.
In the two scenes where Sammy is administering insulin to his wife, he is placing the needle in the crook of her arm, as if mainlining it. Insulin is never injected at this site, but rather at the back of the bicep. The other shots, in the stomach and the thigh, are correct.
While noting down Teddy's license plate number SG13 7IU, Leonard writes it as SG13 71U, which is how it gets tattooed on his leg at Emma's. However, at the beginning of the movie, when Natalie sends Leonard a package containing details about Teddy, the License number mentioned is SG13 7IU. Leonard checks this with the License number tattooed on his leg and does not realize the difference.
Dodd seems to be unaware that Leonard might be in his bathroom, even though the Jaguar is parked outside, Leonard's clothes are on the bathroom floor, and the motel room door has been broken into.
At the diner where Natalie gives Leonard the envelope with John G.'s driver's license, he leaves it on the table when he goes to the bathroom. Leonard would never have left the envelope on the table since he knows that he will forget about the envelope when he exits the bathroom, along with which table he was sitting at or who he was meeting there (which is exactly what happens; a waiter has to hand the envelope to him).
After fleeing Dodd, while driving to the hotel, Leonard is reading the description that Natalie wrote down for him. You hear him 'thinking' what she's written down. He 'says' that Dodd is staying at the Mountcrest Inn, yet it is written as the Monterest Inn.