Hi Linwood, Welcome to the dev forums and thanks for posting! There is no obvious way a user can tell whether a developer's application is in production mode. Some of the applications that are raised to production level ask to be listed in the App Gallery:
https://www.amazon.com/clouddrive/apps?ref_=cd_home_navapi So the applications listed on that page are at production level, but not all production level apps are on that page. Besides, production level still has rate limits, they're just a lot higher than dev level. It is a best practice and strong recommendation that 3rd party apps get production level rates before launching, but it is not enforced.