What happened with Broadwell will be seen as a smudge on his record.
early 15c., smogen "to soil, stain, blacken," of obscure origin. Related: Smudged; smudging. Meaning "make a smoky fire" is from 1860, hence smudge-pot (1903). The noun meaning "a stain, spot, smear" is first attested 1768, from the verb.