Why are my corners "inside-out" in Illustrator?

Question

There are 2 big things I don't get about this image (two identical paths in Illustrator, one of which is reflected, with a pretty simple brush applied to them both in order to highlight the issue)

1. What are these "inside out" corners, and how can I get rid of them? It is nothing to do with the brush because I've seen this happen with very simply shaped paths (i.e. a basic 1-2pt stroke on a triangle) as well.
2. I'm also curious how the exact same shape has a stroke applied in a completely different way. The above shapes are identical except for (obviously) being reflections of one another (this is the above shape deconstructed.

Some notes:
* These are two identical paths (as noted above) with a stroke applied to each simultaneously.
* To make the shape, I merged a circle with a triangle, then adjusted the points manually.
* One is a reflection of the other, so they should be completely (symmetrically) identical.

Answer 1

What's happening is that even though the second shape is a mirror image, the brush is still going in the same direction as it is in the first shape.

A work around is to duplicate the brush to use on the reflected shape. Then with the duplicated brush selected in the Brush palette, go to the contextual menu (the small menu in the upper right of the Brush palette) and select "Brush Options" from the drop down menu.

A new window will open for the Art Brush options. Make sure the "Preview" box is ticked so you can get a live preview if it's working or not. Then in the "Direction" options box are four arrows: Left, Right, Up and Down. Select the one going to the Right. In "Options" box, tick the "Flip Along" box. For the "Overlap" option I selected "Do not adjust corners and folds" which is the first of two buttons.

Click OK and dialogue box will appear with three options: Apply to Strokes, Leave Strokes, and Cancel. Select Apply to Strokes.

Hopefully this works for you. I'm on Illustrator CC 2014.1.0.