In this world you propose, privacy of any sort more or less goes out of the window. But people would grow up with it and so it wouldn't really be noticeable to them. Tinted windows would never get invented, nobody bothered developing encryption for personal use, James Bond is out of a job, etc. So, with that in mind:
1. What would people not hide:
Most things, really. As stated above, growing up without any real privacy would make people pretty open about everything.
2. What would people hide:
Anything illegal, obviously. State secrets and sensitive weapons. All the things with an obviously massive negative impact if revealed to the wrong people.
3. But, how would they do it?
For criminals, simply not looking at stuff is really their only choice. Serious career criminals may take the time to learn to read braille. Taking someone somewhere? A blindfold won't do it, you'll have to use chloroform so they can't see through your eyes either. Making drugs? You'll have to have all your equipment assembled separately by separate, unrelated people in "black box" style units so you can't see what's in them. Counting money? Hire blind money counters, or blindfold the seeing ones.
For states, it's much more complicated. How can professor N assemble super top secret weapon X without anyone seeing? How did he develop it in the first place? They would probably spend a lot of money on trying to build a telepath immune workspace. Would a Faraday cage work? What about heavy water? Can we signal jam this stuff? Failing all of that, they'd probably spend all their time developing highly functional automated robots to do everything, then have Prof. N pass on instructions via a braille computer, with no visual feedback. Make every visible user interface visually confusing to someone who doesn't understand it, random numbers with seemingly no place unless you know where they go.
And everyone everywhere would presumably have a strong culture of doing anything by speech instead of visually.