Hi Paul,
What you are experiencing here is because the two arcs were different polylines. When these segments are not welded together into one, single polyline, when extruded to 3D, they will always leave these unsmoothed edge on the sides. You can try to draw a 24 segmented polygon, PushPull it into 3D and you will see the difference as opposed to a "real" circle.
You can soften the edges with the Ctrl Eraser afterwards -like Chris suggests - and this is most often fine but sometimes, when you have more segments or want to perform more operations,it may be better to weld those lines/curves into one entity. This is what the plugin "Weld.rb" is good - and invaluable - for (I think most "old" users even forget it doesn't originally belong to SU).