It would be worth disconnecting the liquid disconnect/ (coupler if it's a commercial keg) and remove the faucet.
With the faucet off... take it to the table and put it in a pan...take it all apart...taking notice of how it goes together (they're not too hard to figure out) You can clean it with PBW, alcohol, soap and water... just make sure to rinse the parts well before you reassemble.
They make a little brush designed to clean the spout...but you could probably improvise something if you don't have one.
That said...mold grows awfully well in the spout of a faucet. My Guinness tap has thrown some mold gardens out from time to time. I'm getting used to unscrewing the spout...and rinsing the leftover Guinness from the plastic spout assembly. It tends to harbor some leftover Guiness around the restrictor plate and flow straightener. Great place for mold to grow. But if I rinse this drippage off with fresh water...it's not a problem anymore.
Some people keep a small spray bottle with Vodka or Star San nearby to give their faucets a spritz to help cut down on the growth... That's probably not a bad idea. I think water would work just as well. The idea being to flush the beer remnants fom the faucet spout. Beer is a perfect growth medium for mold. I don't think there is anything you can do to keep it from happening...as there are plenty of wild spores just floating around in the air. They just need a warm droplet of beer to land on.
If you have a spare keg...you can put some BLC in...pressurize it...and use it to flush your lines... But even then...it's a good idea to occaisionally take apart the disconnects and faucets for a good cleaning.
