In the movie Memento, a non-linear narrative structure was adopted. What effect does this peculiar narrative structure have on the movie watchers?
The effect of the order of sequences in the film is meant to display Leonard's inability to remember, showing what seems to be a mixed series of events out of order. It is also performed this way because it is a way for the viewer to sympathize and get involved with the story, trying to figure out what is going on as much as the main character is.
It is only when Leonard realizes the truth about Teddy does the movie's B&W and Color scenes (Essentially, the 2 different timelines) converge which is also when the viewer returns to what was the beginning and share in Leonard's realization
I am not sure, this is just a guess: The director might have decided to use this narrative structure in order to confuse the watcher. The main character suffers from a strange type of amnesia, that is why he can't remember the past. We, as watchers, are confronted with the same problem: we see the present, but have no idea of what events lead to this. I think the point is to increase our empathy with the character. What is more, he hides his true intentions(the surprise in the ending).
As from a Christopher Nolan interview, he tried to make the viewers view the story in two different ways. The black and white is what we see from outside. We see Leonard talking to an unknown person. Do we hear what the other person is taking, or see him while the other person is taking in reality? No. So we hear only Leonard, see only Leonard. We move according to true events.
But things start to go a little bumpy after Leonard kills Jimmy. The colour part is what we see Leonard's mind. We also get to know what he is thinking. Like,'Okay, what am I doing?' Or 'Maybe I should search the drawer, although I know I would find nothing'. That is why things we see from his perspective, makes us believe what he believes. We think Teddy is a criminal. We think Natalie as a good friend.
But things are revealed at the end, where we start to think according to what facts are, when we start to see the scenes ourselves, not according to what he thinks. And so the colour scenes go backwards, revealing more and more deep truths, and making us switch from Leonard's own reasoning to our own reasoning.
More information: 18-minute analysis by Christopher Nolan on Memento