I would start with a complete roof reseal if it has not been done in a while but, inspect the roof seams and look for cracks or voids in the seam sealer. This really takes some warm weather as I understand it if using something like Dicor self-leveling lap sealant.
We just bought a 25-year-old class A and were fortunate that the previous owner just resealed the roof last year but, we still found a couple of small leaks after a rain from two other spots, the stove vent fan was leaking on the counter which vents to an outside wall and the upper windshield gasket was leaking on the vinyl dash pad. Both were easy caulking fixes, but we were fortunate to find out all of this before we hit the road. I have had a month to go through as much as I can think of and thanks to those here who helped me. Now, I have emergency patch repair with me as well as a few tubes of Dicor and silicone caulk so I can make at least temp repairs even in pouring rain. Better safe than sorry.
About the age of your unit: We have been asked for pictures of our coach at some parks when making reservations over the phone because they have age limits on RV's. So far we have been accepted because of the condition but, I have heard of some parks that do not make these exceptions to their rules.
If it is old and in good shape keep it washed and waxed and tidy and you may be just fine. Most parks really just do not want a plywood and duct tape covered hobo camp that looks like its been in a demolition derby.
