Memento's backwards narrative can feel somewhat gimmicky, but it forces us to live through Leonard's perception of the world, seeing a scene with no knowledge of the (usually critical) events that lead up to it.
One thing that lends credence to the theory that Teddy is telling the truth about Leonard's wife surviving the attack and it was Leonard who killed her is that even in the heat of their argument at the end, Teddy always specifically says that the assailant raped Leonard's wife, never including that he killed her.
Leonard's story about Sammy Jankis is not only revealing about how Leonard is able to form new memories, it's also possibly Leonard's only real memory of how his wife actually died.
Most of Leonard's tattoos are written in a way that you can read them normally. The tattoo about the man who killed his wife is mirrored. When Natalie points out that the tattoo is backwards, Leonard says "It's... it must be for when I've found him." Leonard doesn't know it, but if he ever finds the killer, he'll be looking at a mirror.
Teddy repeatedly asks Lenny for his car keys or tries to bluff Lenny into letting him drive his car throughout the film, without success. This is because Lenny has recently murdered the expensive and conspicuous Jaguar's owner, and Teddy is trying to dispose of it discreetly, as well as get his hands on the $200,000 inside.
At the end of the movie, you can be left with two conclusions: that Teddy was lying to Leonard, or that he was telling the truth. Which means that either Teddy is a Manipulative Bastard, or that Leonard is taking advantage of himself just as much as the rest of the cast. Neither interpretation is especially happy, but which one is worse?