Black Dots on Shape in Animated Gif Render

This is simply not a good workflow. AE is terrible at compressing and optimizing GIFs due to how its rendering pipeline works. The proper way to do it if you realyl are so concerned about the dithering being so scattershot is to render an image sequence or clip, import it into Photoshop's timeline (or for that matter any other app that offers such a facility), and export it there. Likewise, many online services and free standalone image conversion/ vieewing tools will do a mnauch better job than AE ever could.

Mylenium

Interestingly, I increased the depth to 32 bits and rendered another one with the same settings and it appeared to work. However, when I increased the 7 to 32 bits, I am still getting the artifacts.