Perhaps, as a fledgling Spanish speaker, strolling up to group of Mexicans and optimistically remarking "Estoy muy exitado!" which does not, as many beginning speakers believe, mean "I am very excited." Well, it does, but not in the context generally used in polite conversation. My Spanish teacher said he once saw someone do this.
Other worst conversation starters:
"Sir? Sir! You wouldn't happen to have any heroin on you, now would you?"
Inspired by Oblivion: "Say, what's the fine for necrophilia in this country? Just curious."
"Beautiful day, eh? Too bad Nikola Tesla just came back from the dead with a death ray. Enjoy the balmy weather while you can, my friend!"
My, that last one was random. But I could do this all day....