Since I was visiting Copenhagen for 3 days, I decided a 10 minute walk to Amalienborg would be worth the effort! Actually, since sunrise and sunset was at approximately 4am and 11pm respectively, I made two visits. The first visit was fortunate in that our arrival coincided with the changing of the guard. The second visit was during the late afternoon a couple days later, since I had the Copenhagen Card, I decided I might as well visit the interior of the palace as well.
The exterior is a pleasant white and the symmetry of design of Amalienborg is perhaps its most special characteristic, but like previous reviewers, it would be a stretch to claim any sort of OUV.
The interior of the palace is well-maintained, but there is little on display that sets this palace apart from the multitude of other royal heritage sites in other Scandinavian countries. I agree, Copenhagen may have enough for a world heritage city designation, so perhaps Amalienborg will one-day be an important component of a WHS. Yet, speaking only of royal sites in Denmark, there are at least 2 non-WHS palaces in and around Copenhagen that have comparable value, and perhaps could be better argued for world heritage status. That reality leaves any more Danish palace/castles being inscribed as fairly slim.