Quite the contrary - it means I realize the importance of a second set of eyes. When I read my own written work, I have a tendency to read what I think I've written, and I promise, you do the same thing. This is especially true if what you've written remains in the same format in which it was originally composed.
What does that mean? One example would be the proposals I sometimes write on elance, when I come across a particularly interesting project. The "preview" feature on elance is a godsend, because although the scenery doesn't change that much, it changes just enough that the copy looks different than the copy already established in my mind. Just that minor tweak - it being on a gray background, in a larger box, without a blinking cursor, is enough to manipulate my mind into reading it differently.
So, if you're doing some copy editing of your own work, change the size, style, and color of the font. I guarantee you'll be able to catch more errors!