Hi,
I have been spotting at MEM last year, and it's clear that here are many good places but i highly highly recommend you to stay on the top floor of the car renting range and the parking lot. link below from the top floor, u will have a stunning view of the Fedex cargo, groups of Fedex, really splendid. u can stay there until sunset with different sun locations, and here are restrooms(important:)))
https://www.airliners.net/photo/FedEx-Fe ... YyEQ%3D%3DBesides no worries about the security, the airport security guys would not bother you, and the police is very kind that they will come to ask you "are you ok" which made me very happy. Very true that it worth time spotting there
Have a wonderful trip:)!
Jike