One thing you won't hear talked about much is that Copenhagen serves as the home of the world's most accurate mechanical clock. This differs from the world's most accurate clock overall which is atomic and not based in Denmark.
The clock is on display just inside city hall and open to the public.
Built by Jens Olsen the clock is re-wound once a week, has the slowest turning gear in the world, and is gilded with four kilos of gold. It was first started in 1955 and also displays the location of the planets as well as the stars above city hall.