> Are there some common problems with the rear
> defrost that I should take a look at before
> I tear the whole thing apart?
The most common problem is it doesn't work. Not trying to be a smart #$$ but it is a rare one that does function properly.
First check for power at the connectors on the back window. If no power than the problem (or at least part of it) is in the front of the car. If they have power then make sure the connectors are clean and from there it is likely that either the grids have gotten scratched which breaks the connection or have just broken down over the years.
One of the best things I added to my car was one of the blower type defrosters from JCWhitney. My old grid style one does a small amount of clearing but the blower one clears the view quickly.