Nope, no inspections. Just get it running and get on the road. My maxi actually doesn't have a brake light, just a tail light right now. I need to replace that bulb, and I imagine yours will be just as easy of a fix.
But really, in the city half our riders don't have tail lights at all and we don't get hassled. City cops don't care about mopeds. They've got real crime to worry about. But out in Chesterfield you might want to have everything in tip top shape so they don't bother you.
Me and another guy rode from Soulard to Chesterfield in January. It was 12 degrees outside, and it took almost 3 hours. It was actually a lot more fun than it sounds. haha