Watch the scenes in color, which go backwards in the movie. During the scenes where Leonard confronts Jimmy, and goes to see Natalie at the bar, he finds her by looking at a coaster in his pocket.

The first time he looks at it, it has Natalie in one type of handwriting.

When he goes back (forward in the movie) to meet Jimmy, and looks at it again, the handwriting on the coaster is different.

If it's the same coaster, why does Natalie write her name two different ways???