You need to pull the extra C-clips out and install new ones (or good ones) on the axles.
-edit: A clarification: The grooves must be chamfered either on the axles or in the side gears. You must install the C-clips in the grooves which are NOT chamfered.
The "smooth area" you refer to is the bearing surface on the carrier itself - not the side gears. When the axles rotate at differents speeds there is a speed difference between the carrier and the axle - that's when this surface acts as a bearing. It also supports the axle.
Depending how bad the suface is you might be able to get a way with just fixing the C-clips - if you want to keep the costs down to a minimum.
Kind regards
Tapani
PS Say hi to your mom from the old country
