In the immortal words of Zap Brannigan: Whoopsy daisy!
So I open open the Update manager and just press install updates. When it's finished I just restart and (because I have previously removed cinnamon) I'm promptly left with no desktop at all. I really need to learn to be more careful.
The problem is an unmet dependency libfontconfig1 that caused the update manager to simply remove most of my mate desktop. I installed newer version of libfontconfig1 from debian repos and then successfully reinstalled MATE 1.4. Of course, all fonts now look awful. Still need to figure that one out.