Create shape from vector layer. Gray square.

Long and short answer: Just because it's an AI file, doesn't mean it's necessarily vector based. A lot of features in AI generate merely pixel data like drop shadows, gradients, blends, certain types of using blending modes and transparencies, pattern fills and brushes and a gigazillion other things, including overly complex/ unclean paths as the otehrs already mentioned. Using vectors in AI is a means to an end, not the end-all-be all of computer graphics. With that in mind the resolution to your issues can only be found in AI itself by analysing the structure of the documents and removing or replacing features that don't translate to native vector data in shape layers. That's assuming it would of course even be necessary. Ever since the feature has been introduced way too many people seem to assume that converting to shape layers is a must, not an optional thing. Your artwork could just as well be used as native AI files quite likely a lot of times.

Mylenium

Some illustrator gradients will not be "translated" in After Effects, so you will see those gray boxes. What you can do is to change them in illustrator using any fill color but gradients and create the gradient fills in After Effects.

Perhaps the other layers are very complex to use "Create shape from vector layes" you have to be carefully whit this. Show us with a screenshots your vector graphics.