The good: Communication with the host was very good and prompt. The apartment is very spacious and located fairly centrally.
The bad: The apartment is on an extremely busy street. It is on the fourth floor (no elevator, which is fine). The stairwell is dirty and smells of cigarette smoke. The apartment itself is clearly lived in on a daily basis, and vacated once it is rented out. Many of my minor complaints stem from this fact: Damp clothes left in the dryer, no space in the refrigerator cleaned out for us to use (we made room though), general cleanliness was not quite up to what we expected for the price we paid. Air circulation in the apartment is not the best. There are plenty of windows to open, but at the price of being on a loud street and having cigarette smoke waft through the windows. I would not want to stay here on a very hot summer day...
While we did enjoy our stay, and the accommodations worked fine for us, we would not stay here again if returning to Copenhagen, so it would be difficult for me to recommend this place to others.