I can think of a few ways. One thing they do now is 'sobriety checkpoints'.

Another is the breathalyzer device some folks are court ordered to install in their cars after they get a DUI. It'd be trivial to simply have them in all cars, that can just sample the air, and require no blowing into a tube.

I'm sure you can figger out more ways they could arrange to bust people for DUI given the kinds of surveillance we're already under.