Since the Danish government agreed to let the plane sit there and there is an extradition treaty between the two countries I expect there was oversight and consensus.

Right. Except if there was an extradition treaty and they planned on relying on it, they wouldn't need a plane on the ground and a paramilitary team ready to go?

You would if the Danes didn't want to go apprehend him themselves (I wouldn't if I were them, the news clip would look bad). If he were already in custody there would be no need for a plane and a team, though presumably he would get on some plane at some point if apprehended just as a matter of practicality.

Not as bad as the one where foreign military forces just run around Denmark kidnapping people and imposing their (martial) law over Danish land? I doubt it.

You might not remember those months. US officials forced a foreign diplomatic plane to land on European soil and basically acted like enraged bulls (or rather angry but headless chickens) for weeks. The Danes would have had to do what they were bloody told to do, regardless of how they might have looked in a news clip, because that's what the almighty US wanted at that time, end of story.

It would be fascinating if Denmark and the US have such a treaty, and if that is recent then I would wonder if that doesn't subject Denmark to penalties by other members of the EU and/or other nations in the Schengen treaty. It certainly should.