FooBar41: Good news -
Dell have arranged for a courier to pick up my laptop (at Dell's expense), and will be providing a full cash refund.

In the end, my brand new XPS 13 had the following defects:
1) Two bright spots in the display
2) Flickering display when brightness is set at 15% - 20%
3) Randomly, temporarily unresponsive trackpad
4) Sometimes trackpad produces a right-click, when clicking on the left side
5) Severely misaligned USB ports and audio jack

For other people considering a purchase from Dell -
It was a tough road getting to this point. The customer service representative could barely speak English, often causing ambiguity. They take days at a time to get back to you, so expect 2 weeks to get the problem sorted. However, they can arrange for a technician to come to your property during business hours, and attempt to fix the laptop. If this doesn't suit your schedule, you cannot courier the laptop to their service centre. If you keep nagging (politely) they may give in and offer a full cash refund.

After my bad experience and reading too many Dell horror stories (poor quality control and customer support), I will never buy from Dell again.