It is impossible to tell what is going on from a screenshot that only shows the problem. Pick a layer that you have converted to a shape and then press the U key to reveal all modified properties and start turning things off or resetting until you find what is causing the problem. I suspect it's something in you AI File. If you can't find the problem post the screenshot so we can take a look.
What do you mean when you say "This only happen when there is a Contour activated?" The only reference I find to Contour in the help files is in the description of the Radio Waves and Vegas Effect. I'm not sure what you are talking about.
If you still can't find the problem then try diving into the AI file and examine the layers carefully. Try copying one layer to a new AI file and importing that. If you can make the problem show up with a very simple AI fine with one shape on one layer then detail your workflow, your OS and AE and AI build number and file a bug report that includes the files.
BTW, absolutely the only reason that I can think of to convert an illustrator layer to a shape layer is to use the shape layer animators. Ever since this feature was introduced I see folks mistakenly believing that converting is necessary or that it is a better workflow. Unless you are adding a shape animator it is not better, it only limits the way you can translate your design into video by killing gradient fills, layer masks, and tons of other design options available only in AI.
Your problem seems to be the same as the one in this thread. After Effects engineers are aware of some bugs involving antialiasing problems and artifacts when rendering text and shapes. Those problems affect After Effects CC (2015.3) on Mac OS X. If you would like to help them get some more information, you can file a bug report.
This issue is fixed in the After Effects CC 2015.3 (13.8.1) bug-fix update. This update, available now, can be installed using the Creative Cloud desktop application, or by choosing Help > Updates inside any Adobe application.