The operator asked for my serial number, asked me to describe the problem, then asked if I could be at some address the next day to receive my replacement unit and ship back the defective one. I gave her my office address, and yesterday at around 2PM, a DHL guy showed up with a brand new espresso machine in its package. I lifted it out, replaced it with the defective one, watched as the DHL guy slapped a return sticker on it, and then he left, leaving me a shiny new coffee machine that I brought home in a cab (two people on the street and the cabbie all stopped me and asked me about this beautiful coffee machine and whether it worked as good as it looked and where they could get one of their own). This morning, I enjoyed a perfect cappuccino with breakfast, and ruminated on just how damned good the customer service from Kitchen Aid had been, and I figured, man, that deserves some public approbation.
Update: Canadians beware! Multiple commenters to this post have weighed in to describe nightmarish treatment from the Canadian Kitchen Aid service department, who seem well and truly awful. My experience recounted above was with Kitchen Aid UK.