This is a very exciting time, take lots of notes - you definitely won't remember it all.
Some stuff to consider:
Check every bit of the electronics - play a DVD, try watching TV fore and aft, listen to a radio station. Crank the antenna up and down, turn the antenna booster off and on again. Turn on the inverter and plug something into it - like maybe a TV.
Verify the fit of the entry door. Can you see any air space between the door and the frame at any point when closed?
Check the fit of the front compartment door on your FB - turn on the light inside the compartment and close the door. Then look around the door to see if any light leaks out. If it does, I promise water will get in there. Eliminating this leak has been our single biggest annoyance.
Try all the fans, check to see that they are properly installed at least on the inside - no loose corners, etc.
Turn all the lights on to make sure they work and that all are securely mounted.
If the rig isn't winterized, run water from every faucet and flush the toilet. Also try running water from the fresh tank to verify that the pump works. If you're winterized, check that stuff out ASAP when you open up the plumbing for business.
Have them lift up the mattress and clean off the plywood base of your bed - I promise, it's likely covered in dust. You want that gone before you take the plastic off your mattress.
As others have said, test every single door and latch to see that they work. Slide all sliding doors open and then closed again - even the ones in the bathroom.
Try out the oven and the cooktop.
Turn on the fridge - it won't get cold enough to matter while you're there, but you can see the light turn on when you open the door.
Check the LEDs on both shore power inlets: fore and streetside to make sure they both light up when power is applied.
Check the voltage on the batteries if you can - a trailer that's been sitting on the lot for a while may have batteries that were allowed to repeatedly discharge. If so, you don't want those batteries - you want new ones. Your first clue on this may be that when you prepare hitch up for the first time, the jack fuse blows as you try to raise the trailer's tongue. If that happens, you probably have low batteries; lower voltage causes the jack to draw more current, and that blows the fuse. So, if your jack blows the fuse repeatedly on your first hitch up at the dealer, you may want to ask them to put in new coach batteries before you're willing to take the trailer home. If we had done that, it would have saved us some time later on - we eventually persuaded them to make the battery swap for us.
I hope that helps.