This apartment is really conveniently located for the airport. Christianshavn metro station is a 1 minute walk away, and it's just a few stops to the airport (I think around €8 from memory).
The area by the metro was a bit rowdy when we got there on the Friday evening; lots of public drinking, shouting, men urinating against the wall, etc. Also students celebrating graduating, so lots of hire buses playing loud music, which we could clearly hear from the apartment. Just something to bear in mind - bring a fan to drown it out if you need an early night!
The apartment is huge; it has a whole extra office room which opens out onto a French balcony, alongside the massive lounge/bedroom area, and a kitchen. The bathroom is typically Scandinavian in size; very small, and with a weird shower setup (you turn the tap to the left and it activates the showerhead, which gets the whole room wet. You then need to squeegee the water into the drain).
Found the place well stocked for our needs: even had shower gel and small tissue packets in the bathroom. Wine bottle opener, umbrellas in the hallway, etc. Lots of nice touches!
Check-in was pretty simple, but more involved than other places we've stayed at. You have to phone a telephone number when you land at the airport, to allow time for a representative to meet you at the apartment and physically give you the keys. Lockbox would be more convenient. But wasn't an issue, and was nice to have someone help carry our suitcases up the two flights of stairs!
Thanks for a lovely stay in Copenhagen :)