I think, too, most of the sentences are mistaken for sexism. First of all there are counterexamples like Kvinden er kaptajnen. And second, I always here anti-sexists (I am one, too) that speak up when sentences like "The girls are stupid", "The woman cooks in the kitchen" come etc. But just because we are trying to establish emancipation that doesnt mean that women and men can't do things anymore that were earlier thought to be a stereotype like the cooking woman. Why shouldn't a woman be allowed to cook anymore? It's real fun, just as men can cook, and I've seen Manden laver maden too.
Question for native Danish speakers: In Swedish, this would be translated as "The girls are crazy." "Inte klok" wouldn't be used to say someone isn't smart (rather, inte smart eller ointelligent), but as part of a slightly idiomatic phrase "Är du inte klok?" implying that the subject is doing something outlandish. Is there any of this usage in Danish, or is klog the most common word for smart?
If you're on a Mac, go to System Preferences and then search "Text-to-Speech" and download the Danish voice by clicking the drop down item "Customize…". Select any Danish text, right click it, select "Speech->Start Speaking" and there you go. It's pretty accurate, from what I can tell.