Most of the time when the valve leaks it's due to **** stuck in between the seal and the valve. Clean the poop out with a good brush or take it apart and clean it!
Two valves are for a reason as someone else commented on. You dump the black, then gray to flush.
When at a full hook-up the valves should always be closed until they need emptied or you'll get a giant chunk of goop stuck in the tanks. Leaving a campground you should leave several gallons of fresh water in the tanks to slosh around going down the road. This will help keep your tanks clean