A semi truck swiped the front of my car trying to squeeze through a lane and destroyed my front right headlight. I took it into the body shop my insurance company referred me. They charged me $575 for a used "RT Headlamp assy." When I got the car back, the dynamic headlight control warning came on. I didn't know what the light meant at first and thought it was the service light, so I took it to the Audi dealership, who explained it was an issue with the light and wanted $170 to "diagnose" the problem. So I took the car back to body shop and they claimed they just needed to "reset" the computer after replaced the headlamp. Is that really the case or is it more likely the light came on because they installed the headlamp improperly?

 

First make sure the new light is, in fact, the correct dynamic headlight. Chances are it is. The non dynamic would be a halogen bulb not HID. If so, it needs to have "basic settings" done using a scanner and then aimed while in basic setting. Afterwards, the fault memory(s) must be cleared before the light will function correctly.
Mainly, the light control saw a fault, which set a code in memory and this will disable the function until it's fixed and/or the codes are erased.
The reason for basic setting is so the control module "knows" where the headlamp is aimed at a set point and then it can adjust from there.
I'd say the bodyshop is correct with what they told you.