Hi Steve, I think the most common seems to be leaks around the shower, poor cabling (satallite),lack of info in the manual book, noises from the leveling system & water filter & vacume bags not being installed. There is loads of info in the forum. I love my 36RE but I have had minor problems but they have helped me to get to know the rig. If you have a question, post it in the forum, you will get loads of experienced replies.
As far as checking stuff out, there is a fairly comprehensive list on RVlifestyles website called a PDI checklist - there is a link on one of the forum threads. I reviewed it then just started using everything in the rig & noted what didn't seem right.
Congrats on your purchase, hope you have great luck with it.