smuttiness

noun

1. The condition or state of being dirty: dirtiness, filth, filthiness, foulness, griminess, grubbiness, squalor, uncleanliness, uncleanness. See clean/dirty.
2. The quality or state of being obscene: bawdiness, coarseness, dirtiness, filthiness, foulness, grossness, lewdness, obscenity, profaneness, profanity, scurrility, scurrilousness, vulgarity, vulgarness. Slang raunch, raunchiness. See decent/indecent.

The noun has 2 meanings:

Meaning #1: the state of being dirty with soot
  Synonym: sootiness

Meaning #2: obscenity in speech or writing
  Synonym: dirtiness