That would most definitely be a problem for current law enforcement.
As technology changes, respective fields are going to have to keep up. It will be sink or swim.
I honestly don't know what the future of law enforcement will be when people will be able to do things like change their fingerprints, their appearance, or even their DNA.
One scary thought that is possible with a global nanotechnology network is government monitoring of all of our thoughts and actions. That's just a "solution" that popped into my head first. Obviously, it's not a very pleasant one to think about.
The structures of our governmental systems are going to have to be completely overhauled once these changes start happening.
Thats why I laugh every time I read a book or watch a tv show about the future using retina scans, fingerprints, DNA, whatever as a means of identifying people.
in the end the sole proof of ID will be a synaptic map. and that will have to constantly be updated.