Dumbledore is terrible at doing background checks.

While Dumbledore frequently knew considerably more about what was going on than he let on, we can’t help but think he dropped the ball on a few occasions. Consider all the strange, sadistic, or simply nasty persons who have been hired at Hogwarts. Shouldn’t the headmaster have done more background checks to guarantee that his teachers were qualified?
We’re not saying he should have ripped Professor Quirrell’s turban off to see if Voldemort was on the back of his head, because that would have startled everyone, but come on, guy. Increase your effort.