I will renew my USA passport when I am in the USA. But, my newly issued retirement visa and reentry permit will be in my "old passport". What issues do I face when I return to Thailand. Do I bring both my old passport with my current retirement visa and reentry permit with me?

If you expect to enter Thailand with more than a visa exempt entry you will need them both. As you have a re-entry permit it appears you do not have a valid visa and only an extension of stay so that will have to be transferred into new passport at immigration. Unless a time factor I would get your new passport in Thailand as only takes two weeks and do the transfer before travel as likely to be easier as suspect the other choice is seldom seen.

Yes. As lopburi13 suggests, getting the new pasport here and transferring stamps is the best option. And also, for me, about two weeks to get a new US passport here.

I did this last year with no problems. I renewed my passport while in Canada. Upon arrival in Bangkok, showed new passport and old one with retirement extension and re-entry permit. Immigration wrote in new passport next to entry stamp, and then you visit your local Immigration Office where they transfer everything over for free.