As with any aging trailer, previous care and routine maintenance is extremely important. Roofs are usually good for 10-15 years with proper inspection, cleaning, and resealing. Any water stains or soft spots in roofs, walls, or floors should be considered suspicious and scrutized.
Undercarriage should be inspected as well as the supporting frame work and suspension components. If an excessive amount of rust or corrosion exists, expect to sink some money into axles, springs, and brake assemblies. By the 10 year mark (as with any moving vehicle), components near their end life and have to be repaired or replaced.
Another area of concern for an older coach is the functionality of the water lines. The system should be pressure tested with water. "Was the coach properly winterized year after year?" is a question that should be answered pretty quickly by running the DC water pump. If the pump does not cycle after it initially pressurizes the system, chances are the lines are leak free. You'll (of course) check the city water connection too, making sure the inlet line is not leaking. Checking the toilet seal is a good idea too. If you're doing the inspection yourself, have the seller fill all fresh, gray, and black water tanks to capacity. Then check for leaks in the underbelly. Waste tank gate valves can leak too so check for proper function when the holding tanks are full. If possible, do your inspection at an rv dump. No better way to have a sewage leak show its ugly (smelly) head then when you're doing a normal "post trip" tank dump.
Finally, the electrical components and appliances have service lives too. Hot water tanks will fail (or leak) at some point. Check to make sure the heating element works on electric and the burner lights on LPG. Refrigerator should work on both gas or electric. Again, you should hear the igniter light the burner when in gas mode. Bring a thermometer with you to aid in your inspection. The AC should blow cold air throughout the coach's ceilling vents. Furnace will blow heated air in the floor registers. Check proper function of both.
Other components/systems to check are stove, lighting, battery, converter, brakes, power distribution panel, windows, and awning(s).
This is just a simple guide of what to look for/at with an aging coach. There are lots of detailed documents you can find on the www to aid you with your inspection. Other members may have more detailed insight on each component. There are a couple of RV techs on this site who can probably write pages of what specifically you should look for. Hopefully, they will chime in.
Remember, do everything you can to check the coach before you buy it. Last time I looked, there weren't any lemon laws with 10 year old RVs. Buyer beware, right? And aware you'll be if you do your homework.
Good luck.