I was using a banner template in Illustrator CS4. Please keep in mind there really is no purpose for mentioning that only to say that I am building a banner. I don't think it is causing my problem, but you never know. The problem exists regardless of using a template or not.
The problem I am noticing is that when I go to save to web my 1 pixel border in squares with a stroke of 1 pixel seem to have almost like a shadow. You can especially see it when you zoom when you are on the save screen.
Photoshop does not have this issue and I get really clean lines. I normally make my banners in Photoshop, but being forced to use Illustrator because that is what someone else is comfortable using. Anybody encountered this problem where lines are clean when saving a graphic for web use. Here is an example. It should just be solid black.