So I finally got the chronological order to work on the LE Memento DVD, and lemme tell you, it's a totally different film.
Having seen the movie in its proper format more than a few times, I had come to the conclusion that Lenny was psychotic and, perhaps inspired by Sammy Jankis' condition, tries to convince himself that he suffers from short-term memory loss as well.
Seeing it in chronological order enforces that conclusion, and then some.
Having his climactic confrontation with Teddy in the middle of the film (as opposed to the end) makes everything after that seem more and more premeditated, as if Lenny's challenging himself to track Teddy down. He's consistently snippy with Teddy, even though he shouldn't know that Teddy's "the bad guy" - he sees Teddy a lot, but only once or twice does he consult the back of the poloroid to remind himself that Teddy's the guy he's after. He also "invents" a story about having insurance in order to justify driving the Jaguar, for instance.
**which reminds me - possible continuity error - he also recognizes his truck in the black-and-white part of the film without consulting a photograph**
Also, certain events that I found confusing started to make a lot more sense. In particular, after Natalie gives Lenny the DMV file on Teddy, Lenny removes the poster from the wall and starts to pack up. Which means that he's preparing to skip town right after killing Teddy. (Also, he pays his bill as he leaves the hotel.)
Another scene that confused me is when he hires the escort. In chronological order, it seems to be a conscious effort on his part to re-live the night of the "incident", in order to remind himself to keep going. His burning of his wife's belongings, however, still remains somewhat vague.
Finally, the "new" ending of the film is stunning - in the regular version of the film, his killing of Teddy is done in reverse. But in this version, it plays out in forward motion, so the last image you see is the developed Poloroid, with "Memento" on top.
Curious to hear your thoughts on this. It blew me away when I saw it, and I know I should have written more of my thoughts down at the time, because I know this is somewhat rambly and I know there are other things that I saw that I'm forgetting to put down here...