The problem is that around some corners, the ribbon is very polygonal and blocky. I'm assuming there's a way to up the repetition of rectangles or something like that in order to smooth this out, but I'm not sure where I could find it...?
You probably need to adjust the path spline's type or subdivisions. Setting the type to "subdivided will tell you if that's the issue. If that fixes it you might want to experiment with other settings to get the polygon count down.