I am trying to extrude then bevel a fairly simple shape, but am running into some trouble with the geometry when I try to bevel the edges. The straight edges and corners seem to be okay, but the curved sections don't appear to be smoothing out like I thought they would when I render, resulting is a striped looking pattern around the curved sections. I tried beveling with the modeling tool and the bevel deformer, but I got similar results with both. I figured it was a problem with the phong tag, but adjusting the phong tag properties did not help.
The funky geometry of the bevels is messing up the phong shading, as you deduced. You can improve the result by selecting the edge loops on either side of the bevel and runng the "break phong shading" command.