You probably already figured this stuff out but I just fixed mine so thought I would throw in my limited MBZ knowledge.
The knob is in fact the air conditoner control knob and acts as both a temp selector and at the very far left side of travel a vacuum switch. The not so funny thing is that the knob is actually threaded onto the shaft that has the cutout in it.
So go figure, when you have to turn it off all the way to the left to get the vacuum switch to allow the vacuum actuators to close the vents so that you have heat the know turns on the end of the shaft.
Even better, the vacuum switch is tough to turn so I was driving around in 20 degree weather with the airconditioner on and wondering why it was so damned cold.

Anyway, I opened the center console (didn't know aboutt he little screw through the bottom vent and broke the mount there) and removed the fascia mounting nut from the front of the switch then manually turned the "shaft" counter clockwise until I heard the vacuum actuators throw over the vents. Then I pulled the shaft and knob as you have in your picture. Unscrewed the know from the shaft and applied a small quantity of (you guessed it already?) JB Weld to the threads on the shaft. Screw the knob back onto the shaft. Went to the car and fit the notch on the shaft into the switch and then did a little fine tuning to get the arrows lined up in the "Off" position.
All is now as it should be and I have heat on cold mornings and air conditioning in the afternoon.

Good luck and I hope I made sense.