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Check propane lines (at the propane tank) and replace if they are cracked. You may want to test (soapy solution) the fittings where the rubber lines connect with metal line.
Crawl under the camper and check all visible wiring including wiring to brakes. Also look for any openings that could allow mice to get in.
Wheels should be pulled, brakes inspected and bearings repacked. Check DOT code on tires and replace if they are over 5 years old.
Flush the water tank and lines, sanitize fresh water tank. Also, flush hot water tank and check for bypass system and how it works (valve configuration).
Test fridge for operation on electric and propane (if designed to do so). Run it at least 2-4 days on propane and monitor temperature. Then monitor while on electric.
Fill the black tank with water. Get some "Campers Friend" and add some to the tank so it can help break down any solids. Let it sit for a day or two, then go to a dump station and dump the tank and backflush. Look to make sure water flows freely.
Before taking a trip, sleep at least one night on the bed and find out whether you need a new mattress or a foam topper to improve comfort.
From the picture, I can't tell if you have a roof mounted AC. If so, remove cover and see if it needs cleaning. Then, if you have a circuit that can handle it, see if it works properly.