Hi! welcome to the forums!
First thing to understand is when a new mesh starts, which is pretty easy. A new mesh is started whenever a layer is marked as independent. So you head (with no crown) is not independent is a part of the parent mesh (the root of your puppet). That is, the Head and Body are part of the same mesh. The eyebrows are independent, so start a new mesh. Clicking on any layer in a mesh will show the same outline (the outline for the mesh the layer is a part of).
Once you have that sorted in your mind, this behavior (not a nice contour line) is normally the result of disjoint artwork within the same mesh. If Character Animator cannot draw a single contour line around all the artwork in a mesh, the "Auto" mode defaults to rectangle to not leave anything behind. You can force it to "Contour" in the properties which is the easiest solution. It does not always work, but if it is only a stray pixel or two then its frequently good enough. The real solution is to edit the artwork and make sure everything is connected (down to the pixel level I think!) If you scanned a picture and masked out the background, you might have some unconnected artwork around the edges causing the problem. I use the magic wand or whatever to select the image, invert it, then delete everything outside the main artwork. That does a pretty good job of cleaning up the stray pixels in Photoshop.