This is just the way thick lines look in OpenGL. Instead of using the RMThread render mode, try using a different mode such as RMTube.
Still, your best bet for improving the look is not to have such sharp bends. Define your parametric curve so that it has a smooth transition around corners instead of sudden sharp bends. This is related to the order, but simply changing the order isn’t enough–you also need to define a sufficient number vertices, more than four, and set your knot vector correctly (the default knot vector is already correct).