Was the clip art used in the Illustrator file bitmap or vector?
Each sparkle is made of multiple vectors.
I wonder if I could flatten the (sparkle) layer but keep the transparency so I could make them lighter and darker, on or off.
It sounds like a problem in the Illustrator file. Check those clip art sparkle layers for a stroke or something similar.
Check the problematic layers in the comp by soloing them and then press the u key twice to reveal everything that is not set to the defaults. Make sure there are no layer styles or other effects checked. If all is normal but the art still looks odd open up the footage interpretation, Click the More Options button at the bottom left. and set the anti aliasing for vector art to More Accurate. You can do similar in Preferences>Previews and set Zoom Quality to More Accurate.
Here's another tip for using Illustrator files for video. Any stroked artwork must have a minimum stroke of 1 point or 1 pixel. 2 is better. Fine details in your artwork should be drawn with the snap to pixel option enabled in Illustrator and artwork should be an even number of pixels (points) high and wide.
If none of that works, save out just some of the problematic layers in you AI file and send us a link so we can check out the file or post a screenshot of the problem viewed at a zoom factor of 100% with resolution set to Auto or Full and the properties of your layer with problems revealed.