Yes, you can change individual pixels or sub-full-screen regions. But because the pixels are cells of white titanium-dioxide particles suspended in a liquid, simply writing a new pixel value may leave a few particles floating around.

To correct this, older Kindles and Nooks used to flash the screen all white and then all black before displaying a new page. Later models only do this every few page turns (I think on my Nook Simple Touch it's 6).