What should I do? I had checked tire pressure the day before and only drove about 750 miles when the right rear inside duel blew resulting in damage to the MH and the tow. Only the side wall blew and the tire stayed on the rim. This is the first time in over 25 years of RVing that I have ever had tire trouble. I only had about 14,000 miles on these tires that are less than 2 years old. I bought the best tires they recommended. I will not say the brand but it begins with M.
I had pressure set at 120 psi and they were filled when the tires were cold and had not been driven for over a month, Should I be concerned about the other tires?
Should you be concerned? It depends. Why did the tire fail? If the failure was a sidewall flex failure (sometimes called a "zipper") from running low then there was most likely an active leak, i.e. puncture or leaking valve core would be on the top of my list. In this case the other tires are no more likely to fail next week than they were last week with one exception to be covered in a moment.
If you take the failed tire to a heavy truck tire dealer for the brand involved they should be able to confirm the mode of failure.
Since you were not running a TPMS (tire pressure monitoring system), all we know is that probably sometime between checking the tire pressure and 750 miles later (2 days?) one tire had lost most/all of its air. We also know that the outer dual was run with possibly 100% overload so it probably sustained internal structural damage that shortened its life (months or years). Since we do not know how many miles at what % overload, it is impossible to predict -- so the suggested best practice is to replace the companion dual.
One thing we can do is to use this as a learning experience. With a TPMS a driver would get early warning and many times can stop before a tire is damaged and, by extension, avoid damage to the RV and even not damage the mate in a set of duals. A single warning in the life of a TPMS (years) could save much more than the cost of the system.
Now as to the other possible reason for a tire to lose air. It is possible for a piece of grit to get into the valve core and allow air to leak. I suggest you review the posts on "Valves" (list to the left) and you can see an actual example of a leaking tire and the grit that caused it. So, as I have pointed out in the past, the very act of checking air pressure can sometimes result in a leak and potentially a failed tire.