Harry does not know every in and out of the law, being more akin to a morally corrupt detective of a bygone era. Not only that, but he himself has had some serious issues with errors in judgement. He never once thought of seeking legitimate treatment for Dexter's horrible trauma!  A baby saw his mother murdered and sat in blood. Let's train him to be a serial killer!

These lapses in judgement paint a portrait of instability for Harry, who could never have fully prepared Dexter to be the inescapably clean killer we purport him to be. Sooner or later, someone would have been alerted to his criminal instruction of his adopted son.