The thing about police not being able to do searches without a warrant, etc, it's all well and good, but you'd be naive to think that police are actually bound by this. They might get busted over it once in a while, but you make it sound like there is absolute adherence to rules like this, and from what I've seen and read about American police in particular, that is not always the case.
I snipped this little statement to make a point. Point being that you're showing an immense ignorance of the law and legal systems.
There are three types of law: common law (law that is generally understood, having been established since the magna carta, and encompassing general principles of justice; NOT written down), legislation (Acts/Statutes/Regulations; those laws passed by the governing body), and case law (legal precedent established by the judiciary). Countries which operate using all three can be loosely-defined as Common Law countries. These include the United States, Britain, Canada (except Quebec), Australia, etc. In these countries, the judicial system is adversarial, pitting a representative of the state (Prosecutor) versus the defendant in the presence of an impartial fact-finder (judge) and [optionally] jury. This system is distinct from the legal system used in countries such as France, which operate on the Napoleonic Code. There are a variety of other systems, and I can honestly say I'm not sure what configuration Denmark follows. This paragraph is just background.
Common law countries almost universally have a constitutional provision against unreasonable search and seizure - the wording varies, the jist remains the same. "Unreasonable" is not defined in the constitutional documents, but is actually defined in case law - that is, judges define what's reasonable and what isn't. All searches conducted in accordance with a warrant issued by a person legally authorized to do (justice, magistrate, judge) so are considered to be reasonable unless proven otherwise by the defendant. Supreme Courts in the USA, Britain, and Canada have all said that any form of
warrantless search is de facto unreasonable unless the representative of the state (prosecutor) can establish a reasonable and legal reason for the search. There are many, many provisions in law that allow persons in authority to conduct searches without a warrant.
Contrary to good old "Law and Order," the main point of contention about the reasonableness of a search comes down to what is called (in Canada) exigent circumstances. All Common Law nations have a variety of laws that allow persons in authority to conduct a search without a warrant if they reasonably believe it to be necessary for a variety of reasons (in Canada, there are four). Who decides their belief was reasonable? That's our friend the judge. What happens if the search is deemed unreasonable? A complex weighing of factors that can result in the exclusion of the evidence obtained by the search from consideration in the case.
Beyond exigent circumstances, many statutes actually have provisions allowing persons in authority to search based on specific reasons without a warrant - in these cases, they must merely establish a reasonable belief that the appropriate section of the statute applies. A good example of this is Customs and Immigration personnel. The criteria for reasonable search by both of these entities in most democratic nations is extremely low - else they could not function effectively. Another example is called "search incident to arrest" - meaning that an officer may search a person immediately incident to their arrest for safety reasons. If other evidence is obtained during the search, other legal provisions allow the officer to preserve that evidence.
I think I've made my point.
Police generally adhere to the rules of search and seizure because they have to - otherwise, you risk loss of evidence and staying/dropping of charges. It's not optional, and judges do not treat police officers who flaunt the law politely; the only protection police have from prosecution themselves is establishing that they have acted in good faith and reasonable belief of accordance with the principles of the law. That said, just because a search was not conducted with a warrant does not mean it wasn't legal and the police simply "get away with it" because they can.
The phrase "a little knowledge can do a lot of harm" comes to mind when I read your comments. You may have done some research, but you clearly lack an understanding of the subject material at its core and it makes your argument look naive and overly-simplistic, based more on emotional anecdotes than fact. I suggest you spend some time establishing what the legal facts are before rushing to judgment. You're painting hundreds of thousands of honest, reasonable professionals with hundreds of different departments and agencies with the same tarnishing brush when all you know is limited anecdotes and a simplistic understanding of the legal systems they work in.
I don't know the Danish system; I admit that up front. But if your grasp of it is as poor as your grasp of the other countries you've supposedly researched, it's time to go back and do a lot of self-education.