The Black Swan documentary is primarily about sleazy private sector actors in Denmark. The only remotely state affiliated individuals in the documentary is a business man who was a former small city council member and a bankruptcy lawyer who has previously contracted for Danish government organizations. The system worked fine and the Danish equivalent of the FBI, the NSK, already had ongoing cases of investigations into a lot of the uncovered material.
The only "common" tax fraud in Denmark is when a house needs some minor fixing before being put on sale. Many Danish people will pay their friend's friend to do it for them "under the table" and not as formally contracted and taxed work. This is becoming increasingly harder.
However this is far from the massive systemic corruption in many other countries.