I have 25 inch 1080p monitor, and yeah, I can tell the difference between 720 and 1080 when I am about a foot away. The 1080 has crisper lines. When I am watching anime, most of the time, I am not that close to the monitor so I do not care if it is 480, 720, or 1080. Even when I am close enough to see, I do not really pay enough attention to care.
I should find my old avi and Real Player files from back when I was 12 and downloading off Kazaa. I remember even then thinking that the quality on them was crap. I could see artifacts. Very obvious ones.