Find me now :)
If I were a criminal I would welcome the idea of having everyone in the database. Given that it should be easy to acquire random DNA material I predict a prospering future for random DNA sample gatherers (used condoms anyone?). Do a crime, empty your random DNA sample box and presto, you have just given the police an interesting amount of extra work detaining and questioning innocent people.
Not to mention the interesting possibilities I as a criminal would have to frame specific individuals because hey, the DNA is not lying, now is it. The (public) opinion on DNA as the holy grail for identifying the guilty certainly seems to stimulate such a mindset.
Freedom also means ones government has to put in a fair amount of effort to prove you're guilty. Lets not forget governments have been responsible for more killings in the last century then any other human mayhem so I see a clear need for reasonable checks and balances. One of those would be to be very, very restrictive with the amount of information we voluntarily hand over to our government: you just *know* they will use it for things neither they nor you ever intended. But it is *you* who will bear the resulting consequences.