The biggest concern with regards to the core is water intrusion in the core due to a breach in the fiberglass epoxy layer. The breach could be due to a crack or a hole drilled for some other purpose (mounting something etc). In many cases, a small, poorly sealed hole doesn't cause too much damage as the balsa core is "end grain" - e.g. the grain of the wood is perpendicular to the surface and hence water doesn't wick too far. However, holes that permit the entry of water over a long period of time will eventually allow the core to get wet farther away from the hole. Also, in surfaces that are curved (like the floor) the core is siped (slots are cut in it) to allow it to bend. Generally these slots are well filled with epoxy during layup but sometimes a channel remains that can carry water far away from the hole. For the most part, we haven't seen that issue in C-Dory's.
However, to answer your question about how to detect damage, the best way is with a moisture meter that measures the amount of moisture within a solid. A good surveyor will have a moisture meter and should check the transom and other cored areas of the boat (especially those with penetrations).