How to repair a slow leak in sink food disposal, at discharge
This is a fairly easy repair to make. You didn't say if it's working but I'm assuming it is and it's not jammed. First unplug the disposal. You could have a blockage in there so make sure that there isn't standing water in the disposal.  It's possible that the screw is just loose but I would put a bucket under the disposal and remove the top screw over the tailpipe coming out of the disposal and remove the tailpipe. You'll see a rubber gasket that seals that connection to the tailpiece. I think you'll at least have to replace that gasket. 
Once it's open you'll have a better idea of what's going on. It's obviously corroded. Clean it out as best you can. If everything else looks okay take the gasket along with the pictures that you posted here along to your local home center. They should have that rubber gasket.