Carefully, inspect the TIRE VALVES and any extensions, adapters, extender hoses that might be attached to the VALVES.
If those valves are rubber, they can be a source of leaks and possible blowouts just by themselves. If the valves are rubber and anything more than a cap is attached, they become a time bomb. The weight worries the rubber till it fails.
Go to the Search Window, check Class C, type "metal valve" and read a couple of those threads. Custom brass one piece valves are the Gold Standard but others have been pleased with less expensive and less labor intensive solutions.
Interestingly, the least expensive custom valve kits are DUALLYVALVE sold at Camping World! Valve install requires breaking the tire bead down from the rim, and then the wheels should be balanced.
Find the Date Codes on the tires, as MrB noted above. It's the last four characters of a long string of letters and numbers containing "DOT" and the first two are production week. Last two are production year. So "2612" would be 26th week or June of 2012 making the tires coming up on four years old.