I agree that the hotel badge makes no sense as currently labeled. It would be better if it was consistent with some of the other badges, which measure lifetime achievement. So I recommend it be changed to be total number of nights spent in a hotel in your lifetime.

As for airline miles, the only metric that makes any sense is lifetime miles flown. Of course I can only estimate how many miles I've actually flown because I have not been tracking all of my flights back to the dawn of time, and since AA used to track all miles for million miler purpose they don't have a reliable measure of my actual miles flown before they changed how it works. The only other possible meaning of this could be the MM achievement, although people already put that into their Programs tag.