Looking at a map Burgaw NC would seem to tell me she is a salt water boat. With that in mind problems (rot) should be more of a “from the top down” sort of concern (rot doesn’t really occurred in salt water, the fungus that causes rot doesn’t grow with salt). That said, the typical rot issues would be rain water dependent (fresh water). For this I would start looking at the trunk cabin sides, the sliding window tracks and the wood around the windows, also look carefully where the wheelhouse windshield meets the cabin top and where the foreward windshield meets the foredeck.
Also check the toe rail on the foredeck and where it meets the foredeck.
Check the framing around the hatch openings in the cockpit.
I would look up at the underside of the foredeck up in the forepeak, peeling paint may indicate problems.
Then of course take a flashlight, lift any floorboards in the cabin, stick your head in the bilge and look off to each side below the cabin sole (floor).
Open and look into all cupboards and lockers
Open the engine compartment and lazarette hatch, climb down anywhere you can and look around with a flashlight to see what things look like.
Honestly some water in the bilge of a wooden boat is not unusual. I would turn on the bilge pump and pump things as dry as possible then look around everywhere, you may well be able to follow the trickle of water to its source.
one downside of being a salt water boat is that the fastenings will suffer more than if she were a fresh water boat. At this age she may be due for some refastening below the waterline (would use bronze wood screws). This may be the reason for water in the bilge.
as to your question about 1/2” plywood being heavy enough,...... Honestly, Owen’s of that era were lightly built boats that were entry level boats. She is not a boat that you would want to take offshore fishing out at the canyons.
She is however still a survivor and a nice little cruiser that is basic enough and light enough on systems that she would be manageable for someone who wanted that type of boat.