Well since you're buying new there are differences in what I'd look for.
My dealer where I purchased for example gave an EXTENSIVE walkthrough of our unit. Every single button, switch, valve, door, seal, and gadget was shown to us to be working and then we were able to walk around and push and poke and wiggle things ourselves.
For us that easily covered alot of the small fixes that some owners have to do upon first having their pods, that isn't to say there aren't things that can be missed because for sure there are but you have a great list started.
I think all of those things would put you well on a proper shakedown check of a new Pod. Considering we had an issue with our fridge when we first bought it, a future RV purchase I'd probably bring my digital temperature gauge with me along if I ever bought a new RV again. I'd like to see a proper cooling temp before I walked out the door.
Make sure they run all your appliances in ALL modes for you, be sure to listen to your propane regulator to ensure it isn't pinging before you take delivery. Although this seems to have been corrected and I don't see it occurring with new owners anymore I'd still make sure on that.
Pretty obvious but make sure hot water comes out your hot water taps and not vice versa as that has happened before.
That's about all I could add or think of. Congratulations and best of luck on your shakedowns!!!