Jesus Christ, you want to pick up a little Danish from an easy comedy, and you pick Klovn? Klovn is some hardcore shit, dude... That's pure, weaponized cringe right there.
If you want something a little less painful, there are plenty of good Danish movies to pick from (I'm not really versed in their TV shows outside of Klovn). They're all a little, well, weird, but that's just Scandinavian culture for you. I'd recommend Adams Æbler and Blinkende Lygter, or if you want to check out some of their animated movies, there's the essential Terkel i Knibe, as well as Ronal Barbaren and Rejsen til Saturn.
As an aside for the non-scandis out there; while Danish, Swedish, and Norwegian are all quite similar in their written forms, the spoken forms of each language differ quite a bit more. Danish differs most of all, and is probably the hardest of the three to learn how to pronounce correctly. I speak Norwegian and never spent much time on Swedish, but I can understand enough to keep a conversation going, and I can do a fairly decent pronunciation of a few basic words.
Danish, I just make a few guttural noises and hope for the best... And I can't understand a wild Dane worth a damn, especially not when they go full word-avalanche. So if anyone feels like they're having a hard time with the language, you're not alone.
Then again, that's not even touching on the subject of dialects... I don't know how bad Danish is with this, but both Norway and Sweden are rife with various dialects that change things to the extent of effectively being an entirely different language. When I was in the military, we had one fellow in the platoon who quickly made a name for himself by being completely unintelligible. Not even his roommates from the same general region could understand him, at least not once he got a couple pints in him...
And yeah, there are a lot more similarities between English and Danish/Swedish/Norwegian than with, say, German. There was a lot of Nordic influence on Old English, and some of it's stuck around through the ages.