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Insist the dealer connect to AC source.
Insist on two quality (like Interstate) deep cycle batteries are installed.
Insist propane tanks are full and check for propane odors anywhere.
Inside;Get a full demo how each every thing works.
Make sure you get the books for each appliance, tv, stereo etc including the owners manual.
Open every drawer, door and slide panel and inspect it for proper construction and mounting.
Check every system water heater on both modes, gas and electric.
AC (both) and furnace. Check all modes of the AC also.
Check proper operation of the TV's and that the stereo is actually hooked up.
Look at the carpet, mating surfaces, tile, etc.
Turn on the water pump and check everything for leaks and that the water heater is working.
Check windows for sealing and operation. Make sure you understand how the escape windows open.
From previous problem posts, make sure the shower is sealed all the way around.
Open the C/B-fuse panel and (power off) and check for loose connections, bare wires and pieces of wires left inside.
Check the slide operation and understand the procedure. Go over it until it sticks.
Do the slides go in and out smoothly? Binding? Creaking or does it just not sound smooth?
Anything in contact with slides? Rubbing, interfering?
Slides can scrape the carpets and floors. Look for marks and scratches.
Outside;
Wear some old clothes and get under your rig and look for anything that is not right like drooping bottom panels, cuts, handing wires, etc.
While you're under there, look at the suspension and brake wiring or hoses if EOH brakes are installed.
Spring shackles, axle to leaf spring u-bolts, etc.
Let your eyes drift to everything and check anything that just doesn't look right.
Tires, cuts, proper inflation and most importantly the date codes! Don't accept it if the tires are more than 18 months or so old. RV tires age out before wearing out and 5-6 years is the most often max on age before replacing.
Check the finish for dings, dents, improper panel matches, etc.
Storage areas and doors for things like sharp edges, loose panels etc. Also the reported loose latches.
Open the wet bay and the filter access and with the water pump on, look for leaks, hoses that are chaffing.
The water pump should not be excessively loud if properly mounted.
Check coax cables, wiring in wet bay.
If possible, verify the cables are actually connected. The easy way to do it is to installing a shorting cap on the outside connector and check resistance at the proper inside connector both front and rear TV. Turn off the AC before doing it just in case. Resistance should be very low, if it is infinity, get it fixed before you accept it.
Since (in theory anyway) the tanks are clean and dry, run some water into both grey and the black tanks and cycle each valve.
Have the dealer demonstrate the leveling system as many times as it takes for you to understand it
Inspect the pumps, hoses and jacks for leaks. There have been a few reports of blowing fuses on the hydraulic system... if it pops, make them get it fixed.
Get on the roof and look for low points, improperly sealed vents, ac mounting, lap seams, front and rear cap to roof sealing.
Most importantly DO NOT hurry! Don't let the dealer rush you either. Go early and take your time. Being in a rush to hook up and go is much like a pilot skipping through a check list and finding out the fuel tanks weren't topped off by the last pilot... Happened to me twice, once I found it by proper pre-flight, once by a lucky gauge check after engine start. Taking your time prevents you being upset later. You want your new rig, but getting it right the first time will make you much happier.
Here is a link to a good PDI checklist
http://www.rvlifestyle.net/id20.html
Remember, do or don't be forced to rush... You'll be happy you did.