All phones could be mandated to record audio/video at all times and stream it to government servers for archiving and processing, for example.

And you could set up society so that you'd be useless without carrying your phone, as we're most of the way there already. Not streaming your complete data to the government would become a crime.

All public places could be recorded in a similar way.

If you combined it with satellite tracking of the whole planet, you could even identify people that have chosen to go off the grid for some period of time, so you could solve crimes that happened in the forest if you want.

That's pretty close to perfect surveillance.

I can't think of a crime that couldn't be solved this way, but it's not a society where I'd want to live.