Qataa’s crime:
He was overheard saying: “Even if the Prophet Mohammad comes down (from heaven), I will not become a believer.”
It was even more trivial (and sad) than that. The kid was working at a coffee shop, and refused to serve rude customer, jokingly saying "Even if the Prophet Mohammed returned and told me to, I wouldn't serve you!" So he was beaten and executed for taking the prophet's name in vain.