Dave Stohler, one of the main characters, is obsessively interested in bicycle racing and the Cinzano team in particular. About twenty-four minutes into the movie, after he's learned that the team is coming to race close to where he lives, there's a scene where he rides his bicycle down the highway as part of his training. The fourth movement of Mendelssohn's symphony is used as the soundtrack here, and its "presto" tempo marking matches the ever increasing speed at which Stohler races and his urging himself to go "Faster!"
The other realization I had is that there's something of a similarity between Stohler's pretending to be Italian and Mendelssohn's writing a symphony inspired by Italy. Of course, these aren't exactly the same, but common to both is this looking to a foreign culture. Neither is the genuine article: Stohler is American, not Italian, and the "Italian" symphony, unlike some of the veritable Italian music used in the film's soundtrack, was written by a German.
