It's been a long time since I took modern physics, so I'm not positive, but I think you're right that the moon would have time moving slower, and if your 50ms/day is right (edit: I based this on the moon traveling faster than the earth, but I don't know anything about gravitational relativity, so that's probably wrong) then you'd need to do something like skip a second every 20th day on the moon to keep pace with Earth. We could call it an "anti-leap-second"

Programmers, that seems pretty simple; what's the big deal? ^/s^