Show that this algorithm does not work for determining convex polygons
A simple counterexample is a pentagram (http://en.wikipedia.org/wiki/Pentagram). It contains right turns (if you go in clockwise direction) only, but it is not convex. The above algorithm will incorrectly say pentagram is a convex polygon. It's actually a complex polygon. 

In other words, algorithm might fail if the input polygon is complex.