I can't top some of these, but my new boss is the most clueless guy I've ever seen. Short conversations and emails are like interacting with an ELIZA machine over a noisy channel:

Me: "I'm talking to the guys at Verminous about the frangle, it has some problems."

Him: "The frongle is very important. If there are problems with it, you should contact Vomitous immediately."

Me: "Ok, will do."

All in all, this works OK for me. Meetings and longer conversations do not go as well, unfortunately. One of us--or often all of us, taking turns--will try to explain some basic thing about our latest database project. He doesn't get it, doesn't get it, doesn't get it. Finally he seems to get it, or pretends to. Five minutes later, it becomes clear he was actually talking about the company picnic.

Have you guys seen Monty Python and the Holy Grail? The scene where the king is trying to explain to the guards to "stay here and make sure 'e doesn't leave"? It's like that.

I don't know how this guy gets his pants on right way round in the morning. So far, he has not actually engineered any disasters, but it is only a matter of time.