Apparently one reason that the famous "419 Scam" spammers write such illiterate and instantly-recognizable spam email is that this serves to filter out all but the most gullible recipients. By writing badly and unconvincingly, they ensure that more of the people who actually respond are gullible enough to be pulled in to the scam. Because it's cheap to send out millions of copies of a spam email, they have a strong incentive to minimize the number of responses that aren't good leads.

Are there other cases where someone might do a deliberately bad job at convincing people of a falsehood, in order to filter for the most gullible or susceptible marks?