More dumb stuff from pilots than ATC though did get a kick when the ATC one day was talking to another pilot and started the call with "To help our 1950s computers we are trying to bring into the 1980s...."
Haven't heard anything dumb from ATC but there's one time you can tell the poor girl was beyond overwhelmed--probably a trainee. Lots of respect for those at SoCal tracon and the various towers. The sheer volume of traffic that they sometimes have to keep track of is pretty impressive. Also it was quite heartwarming the other day when John Wayne tower asked us if we plan on doing a practice approach into another airport after we went missed, and gave us vectors accordingly.
I just heard a funny one the other day. A VFR aircraft was requesting the weather from their destination. So the controller goes and reads the METAR but leaves out "few clouds at FL240". The aircraft is VFR at 095 so no where close to the flight levels not to mention they cant go there without a clearance anyway. Someone is the control room rags on the dude saying "what you're not going to read the few clouds to him?" Out of guilt he keys back up and says "N12345 there are also few clouds at FL240". The pilot was fairly confused by the transmission "Uhhh Thanks Center but we are at 095".