Inspect the roof for water damage. If your RV doesn't come with a ladder, you may not be able to get on the roof without doing damage. If your RV does have a ladder, carefully climb to the top and make sure there are no leaks. Seal any seams or fasteners that may allow water to leak into the RV.
Examine all body seams. Apply sealants that are appropriate for the body type.
Notice any wrinkles or discoloration in wallpaper. Regularly feel the interior walls for soft spots especially near any area that has cutouts such as vents. Also, check out the joints where the walls and ceiling meet.
Access the utility panel and examine it for any leaks. Go inside and check the water heater, furnace and shower stall. Feel around drain openings to make sure there are no water leaks there.
Look inside the cabinets, both overhead and floor. Inspect the inside storage compartments as well. Do the same for the outside storage as well.
Pull up the mattress. Make sure there are no soft spots indicating water damage there. Cab-over bed areas tend to have more problems with leaks, so don't forget this step if your RV is a cab-over.
Determine that the exterior surface is not peeling or warping in any way. Look down the side of the RV. If you see any bubbles or ripples, you may have a problem with water between the side walls.