Update!

Haven't updated in a while, but the intern's last day was last week. 2 weeks before that, we told him when his internship would be ending.

As soon as my manager gave him the news, I got this email from the intern:

Can I speak with you for a few minutes?
(as in the moment)

Not sure why he had to specify "in the moment" but I told him to stop by. He asked if he did anything wrong, and boy was it tempting to give him the laundry list. I couldn't bring myself to do it so I just said that there wasn't much work to give him at this point.

Which was true--there was no work for HIM, but if we had a competent intern there would have been plenty of work. Over the last few weeks all four of us had stopped giving him work because no one felt like wasting time re-explaining it 10 times only to have to fix it ourselves in the end.