TIRES NEED TO BE CHECKED.
Tread is not an indicator of tire usability.
If they are over 5 years old they need to be changed. 
You chance major damage from a blowout.
(Can I get an AMEN)
Before moving very far > 5 miles I would repack the bearings specially if you plan to go  highway speeds
Inside
Fridge can be a major expense. Over $1000.00 to replace a typical gas/elec fridge.
Is the fresh water tank a pressurized tank or a tank with a water pump on it?
Some of the old metal tanks pressurized developed pin hole leaks requiring replacement.
Is it a wet bath or dry. Wet bath the bathroom gets wet during showering and a dry has a separate shower pan. People tend to get tired of wet baths quickly specially if they have children. 
Common water damage spots are the floor by the door and the front corners of the trailer. Be specially diligent in these arras