The sentence subject is in bold. The misplaced modifier - as one of cinema's most recognizable faces - doesn't quite fit.
As one of cinema's most recognizable faces, Buscemi's many credits in some way chronicle American independent film, from Jim Jarmusch's "Mystery Train" (1989) to Quentin Tarantino's "Reservoir Dogs" (1992) to the Coen brothers' "Fargo" (1996).
It's a good idea to take a second look at any sentence that starts with "As." Unless you're careful, it's pretty easy to slap on an inappropriate modifier.