Moonlighting is not a problem as a GMO, command permission is required but is rarely an issue. The most common are the "Doc in the Boxes", they'll hire people with only an internship if you can get licensed in the state. Some people picked GMO tours based on their ability to moonlight in a certain state...about half require only one year of GME, others require more. Once you're licensed, you are allowed to practice "medicine and surgery", more than phlebotomy though insurance can be a problem. I know of people pulling down an extra 40k a year moonlighting while GMOs, though that's unusual. Around here, you can make about $40/hour in a DITB.
You cannot moonlight while in a DOD residency, their opinion is they pay enough and you need to be studying. I think that's fair.
I don't moonlight, I'd rather have the time off and I'm not a primary care kind of Doc, so my time as a DMO is plenty of patient contact. I like the active duty population, but beware of the civilians...they seem interesting when you're a med student, the adjectives change when you get out there.
DD