To make foul or dirty, this instance of “be-” forms the verb out of the adjective “foul”.  In the 13 and 1400s, this word slowly replaced “befile”, an interesting formation of be-defile.

• 13.043 and though all was befouled and blasted

I note that the filth that one is covered with when befouled often refers to metaphorical moral filth.  All in this passage has been befouled by Smaug’s coming and goings – and also his malice?  More on the malice of dragons in Legard.

“befoul, v.” OED Online. Oxford University Press, March 2015. Web. 7 May 2015.

Legard, Sara. “Essential Dragons Beyond Tolkien’s Middle Earth”.  Mythmoot II Proceedings.  Mythgard Institute. Web.