Oooh yeah, Illustrator is a tough program to use if you want to try and achieve a hand drawn look. However, I love working in vector because no quality is lost if you need to scale up an image. If your interested in looking at other programs, I'd highly recommend Manga Studio. The program really caters to comic making, you can hand draw easily in vector (that's what I use for my comic Oops), and you can add color, customize brushes, add effects, just an awesome fairly cheap program. The eraser tool alone has improved my life, by being able to erase whole overlapping sections of lines with a swipe of my wacom pen.
But yeah, I agree with most of the other comments that the pixels in the image is probably caused by abode's Save for Web option and then messing around with the compression settings.