Leonard is from San Francisco, while the film appears to take place in Southern California (Teddy is constantly urging Leonard to go back north). Yet Teddy—according to Teddy, anyway—was the chief investigator of the rape-murder. So did the rape not take place at their home in San Francisco? Were they traveling at the time? If so, it would seem that Leonard's wife travels with many favorite possessions, including an old teddy bear and an antique clock (we see them in the flashback). Also, for someone in a strange city with short-term memory loss, Leonard is able to get around fairly well. He's got the big map, sure, and he asks for directions once, but he's able, for example, to beat Dodd back to Dodd's motel room.
JoePantolianoplays the most trustworthy character in the film?
Actually, this is less plot hole than inspired casting move. Pantoliano is always playing scumbags—from Guido the pimp in Risky Business to Ralphie in The Sopranos—so we expect him to play a scumbag here. He doesn't disappoint, but in the end (or the beginning) he turns out to be the most trustworthy character in the film. He uses Leonard, sure, but he also tries to help him, revealing the truth about his past.
IfLeonardhas short-term memory loss, how does he remember ... ? (Part 2)
Throughout the picture Leonard recounts the story of Sammy Jankis, a man with apparent short-term memory loss who accidentally kills his diabetic wife with an overdose of insulin. Yet, according to Teddy (and a few frames of flashback), most of this isn't Sammy's story at all; it's Leonard's. Leonard's wife survived the assault. She was the diabetic. She was the one who tested his short-term memory loss by demanding extra shots of insulin, which he gave her, and which ended up killing her. Leonard has such trouble digesting this information that he decides to cover it up by killing Teddy. (Click for a more detailed summary of the plot.)
But if the second half of Sammy's story is actually Leonard's, then Leonard shouldn't remember it, since he was already suffering short-term memory loss at the time. Yet he does remember it; he tells it incessantly. Of course Teddy could be lying about the whole Leonard-Sammy connection. But a flashback (Sammy in the ward becomes Leonard in the ward) indicates that Teddy's being truthful here.
What is memory anyway?
There are several ways that writer-director Christopher Nolan could explain these plot holes. Here's one: If Leonard repeats something enough, he can condition himself to remember it. That's how he remembers he has short-term memory loss; that's how he remembers his argument with the cops about the second rapist. Unfortunately this means the story is reduced to "He can't make new memories—except when he can," and the already-murky plot turns to mush.
A better—and by no means mutually exclusive—argument is that Leonard's condition isn't physical at all but psychological. Leonard is capable of making new memories and does, at times (he remembers the insulin story, although the protagonists get smudged, as if in a dream). Mostly, though, he chooses to forget everything in order to a) bypass pain; and b) give his life meaning. But if his condition is a defense mechanism brought on by his wife's rape, shouldn't he have shaken out of it before the third insulin injection killed her? And if his short-term memory loss was brought on by the pain of his wife's rape, why does he choose to remember the rape? Is he torturing himself? Is he torturing us? And is his memory loss after his wife's death different than his memory loss after his wife's rape?
More and more, Memento looks like an Escher painting. If the source of the waterfall is the pool beneath the waterfall, how does the water flow up? If Leonard can't remember (except when he can), and it's all a defense mechanism to avoid painful memories (except for the most painful ones), then when did he begin to forget? And why?
We hope this clears everything up.