Don't worry about the dropped chain. Even though a bike shop can properlly build a new bike for a customer, once you start riding it, the bike needs a little "breaking in" time. The cables for your deraileaurs and brakes will strech out a bit and fall out of adjustment. This is a normal thing. Once you bring it back to the shop for the gears and brakes to be readjusted, everything should then be fine as the cables are now stretched and ready for action.