Denmark has much stricter laws for privacy than USA: Companies are not allowed to sell your address or phone number to other companies. So Danes don't mind giving Blockbuster their address because they know it won't be sold to 3rd party.
Also a Danish social security card (the kind you show to doctors or hospitals, so you take it everywhere) contains your full address and the CPR number. Handy if someone finds your wallet, so they can bring it back. Unless of course they want to screw you over, because all relevant personal info is on that single card.
If you find a Dane's wallet, you can basically do any kind of business on their behalf that doesn't require showing a picture ID.
That is correct. Unless your address is "protected" a large number of companies with access to CPR can look up your address. No privacy to speak of there.
Yes, the Danish social security card contains the CPR number (SSN).
A big (huge) problem in Denmark has been created as an unintended consequence about fear of "having a number assigned" to you. As a result of much debate in the 1960-70's, the compromise was to designate the CPR number as "confidential". Which was really, really stupid in the first case because 6 digits out of 10 is your birth date, one is a check digit, so in reality you have very, very limited entropy.
But worse, because many confused confidential with secret, misguided companies (and authorities) started using it as an authentication method. The logic being that since 3rd parties were not supposed to know the "secret", proving this knowledge was taken as proof that you were who you claimed to be.
Even today, it is amazing what you are allowed to do with a CPR number. So yes, it is foobar.
Other people aren't supposed to know your SSN.
A former police officer who was fed up with the poor security surrounding some online government service managed to extract and publish the prime ministers SSN and got in a lot of trouble.
Companies publish their SSN on their websites.
The key for recipient in intra-country payments is account number plus SSN.
Identity theft is rare. I've always found strange reading about credit card scams in USA where people go through your garbage and get a credit card in your name. Here you'll have to show up in person and identify yourself.
No one uses it.
But then again, Danes never seemed to care much about privacy (you can look up a person's address and all kinds of personal data if you know their social security number, for example), so I doubt there's going to be much backlash.