You'll want to contact both the installer and Leviton. The installer may subsequently contact Leviton on their own accord. Dimmers catching fire are a very serious issue that the manufacturer should immediately be made aware of. No doubt, Leviton will likely want you to ship the dimmer to them for their inspection of the failure.
Solder land where that (former) black wire connected failed. Maybe a bad dip job. Looks like a lead from a filter choke, wider view would clarify. Choke leads tend to be solid wire, which draws heat away and can be problematic during manufacturing.
I agree with MNicolai. With a failure like that on a 3 year old product the cause of the issue should be for hte installer or manufacture to figure out. The good side of that is hopefully they'll give you a good deal on a replacement.
As a side note after your done with a painstaking task of cleaning up all that dry-chem look into Halotron I "Clean Agent" Extinguishers. They're a bit spendy, but they're totally worth it.