As a reader I don't care much about them, or even take notice, unless the error is really blatant, or was a major part of the character/story/environmental design. While I'm stingy on stylistic quality I don't see continuity errors as a deterrent, we all make mistakes.
As a creator, not really? I make continuity errors all the time in my comic, usually because I forget the little details, sometimes remember things incorrectly. My reaction is basically "oh, whoops! I've messed that up. Lol." Of course none if the mistakes I make affect the story or characters, so it's not a problem for me. If it were to have an impact on those things I'd redraw the page, or fix it to the best of my abilities.
Funny story. The worst error I've made so far was when I decided to draw a page while having a major sinus infection. Being extremely out of it I got confused on the layout of the setting, and totally drew the wrong background for one of the panels. After recovering I realized the error, being completely amazed with my lack of comprehension at the time.
I finished and posted the page anyway.