The trouble with greylisting

Greylisting is one of several fairly common methods of preventing bulk spam from getting into a mail server. In short, the concept is based on the following idea: The receiving mail server is contacted by a sending server it has never seen before. Rather than accept the (possibly spam) message, it issues a message to this effect:

Dear sending mail server: I'm having a problem right now, and can't accept your message. Please try again later.

The thought is that, if it is really serious about delivering it, it will try again in a little while. Most bulk spam mail servers are not configured to retry. as they expect that most of the harvested addresses they attempt to deliver to are going to fail for one reason or another. A real mail server, however, will try back after a few minutes. At that time, the greylisting server will (in theory) recognize the retry attempt, accept the message, and make a note never to test that host with this rather rude procedure again.

There are at least a few problems with this method, that I have seen.