I've come across this weird issue.
I have two layers I want to render and combine. Those were set up with the "Setup Tracking Scene" button. The first layer always renders without problems. However, the layer that contains my shadow catcher renders with the top of each render tile's top missing, or artiffacted (based on what tile size I choose). But when I turn off rendering for the first layer, the second one renders fine. Also, if I render on my CPU, everything renders OK, but it takes about twice as much time (I'm using an old Athlon II).
Here's what the scene looks like:
And here's the background layer rendered:
I'm using cycles in Blender 2.78, on Arch linux. My GPU is an AMD RX 460.