First up, it's worth making sure your curve is clean before attempting to stroke it. It's a bit of a pain to go through and clean up every single curve, so it might be easier to sketch in a shape with the brush tool and then quickly trace it with the standard pen tool. (I didn't do that here, I just removed any points that caused jolts)

Secondly, you get a much smoother transition if you turn on "simulate pressure" when you stroke the path. The problem with using the simulate pressure option is that it thins the brush stroke to 0 pixels wide at the ends, or at one side of a closed loop, but this can be countered by setting the minimum diameter under Shape Dynamics in the brush control panel. I'd recommend keeping it somewhere around 40-50% as the smoothness diminishes the closer the minimum gets to 100%.

Hope that helps!