An Immigration Minister that is keeping people out unless they fit his special criteria and refusing to allow a British MP in on, (as far as I can tell) grounds that limit freedom of speech.
A Minister of Heritage that doesn't know his file.
An Environment Minister willing to sacrifice the environment to get pet projects underway.
Our Foreign Affairs Minister just got back from Afghanistan where he apparently investigated whether or not torture was still occurring in the prisons. He did this by asking a prisoner while the warden stood beside him.
There's more I'm sure, but what I've noted here happened this week alone! So, why don't we go straight to the leader of the pack. The most incompetent, because after all, he named them all Ministers didn't he?