What are toffee potatoes?
I think the toffee potatoes in the article must be Brune kartofler; the literal translation is "brown potatoes". They are simply small potatoes covered in caramelized sugar. The photo Ocaasi links to are potatoes gone terribly wrong. I think the photo caption is ironic.

They are a traditional side dish for any christmas meal with pork roast or duck. 
Here is a video that shows how they are made: http://www.youtube.com/watch?v=LYoJ14RIIhs.

The recipe is as follows:


Boil small potatoes.
Peel them.
Distribute sugar evenly in the pan.
Warm until the sugar caramelizes.
Add butter in small pieces (amount of butter and sugar are equal).
When the butter is incorporated add the potatoes.
Distribute the caramel over the potates.
After 10 minutes the potatoes are done.
They should now have a nice layer of caramel around them.