The end result of a Zero-privacy culture is not determined by how much information is available, but by how that information is used by the organizations who are most interested in it.
You can't have a zero-privacy culture and assume that criminals aren't going to abuse it in some fashion. Even with an infinite wealth of information available to everyone, criminals will find minor ways to 'trick' the system into going blind for a second, or reporting false information, and with the level of trust people have in the observation technology that's available, the effects would be devastating.
Small-time criminals would find their lives much harder - with petty crimes like theft being easy to prove, and murder being immediately solvable. Digital crimes would be easier, with simple ways to trick the system being justifiable as it is today - by 'finding ways the system can be tricked to solve the problems the system has today', such that cyber crime would become much more popular.
And of course, even with a wealth of information at our fingertips, our real limiting factor on how much crime we can prevent is how much of that information we can act upon. Certainly there will be video footage of every minor crime taking place, but unless someone is monitoring every surveillance camera in the world (and there would be a LOT Of them) 24/7, there's no guarantee the criminal will actually be caught.
And there will always be crimes where the intent is misunderstood - unless this surveillance system also infiltrates and reveals a person's intent. In which case, we'd have a Minority Report situation, where people are arrested for crimes they haven't yet committed, which would bring about its own problems.
The government would be an early adopter of this system, and it would certainly use this information to help law enforcement keep any society that uses this system safe. We've already established that in the Criminal section.
However, there are so many other ways for the government to use this information - some justifiable, others very unjustifiable.
Assuming the universal surveillance goes across boarders and isn't limited to one country, the government would use this technology to spy on other governments - and if other governments are using this technology too, we'd have a complicated network of governments spying on other governments, who know they're being spied on by the other government. In short, no more state secrets of any kind (Unless they use blocking technology: See Criminals). For governments with like-minded goals, this would be no problem. For governments that are mortal enemies, this would be an absolute nightmare.
And that's just what the government would do outside their own boarders. From within, the situation becomes much more horrifying. Opposing political parties would have full access to all the strategies and secrets that each party is forming, and full access to the lives of their voters, which would lead to incredible levels of pandering for each government body, and an incredibly high focus on major political candidates to not create any scandals. In this world, political success would hinge entirely on creating a perfect self-image. Whether or not this creates a perfect politician is questionable, depending on how well they can form this illusion, and what they actually do with the immense power of all their nation's personal information once they're in office. If their intent is pure, there's no problem. If they intend to abuse it, they'll have no problem abusing it at all, save for justifying each abuse as it's exposed by the media.
You say that there is no privacy, and if that is true then there'd be no privacy among neighbors either, or even among strangers living far across the planet.
In some cases, this would be fantastically useful - you'd instantly know if you can trust someone or not, and you'd know if anyone does anything unfair or unkind to you without having to wonder or worry about it at all.
On the other hand, any minor mistake or mess-up that you do would be known to everyone, everywhere, forever. People would be much more cautious, they would take much fewer risks, and we'd be held much more accountable for each individual action.
Assuming we don't manage to greatly reduce criminal activity, the imprisonment rate would skyrocket at first, until we all grow to adjust to being constantly monitored, or learn to avoid it in any way possible before committing any mistakes, which could still get found out and land us in prison and permanent ridicule for the rest of our lives. The common citizen would be constantly vigilant of what they do.
On the other hand, as we mentioned earlier, the average citizen wouldn't spend their whole life looking up what each individual person has been seen doing, and wouldn't have time to learn everything about everybody they encounter casually throughout the day. Clean-looking, honest-looking criminals would pass right under their notice, simply because information overload would prevent anyone from meaningfully using this information, except on their close friends and colleagues.
Corporations would definitely come out on top in this world - universal knowledge of their market, and what the market wants most at this very moment, means knowing exactly what to develop and focus on at any given time. And say goodbye to ever having to worry about hiring new employees ever again - you know instantly the qualifications of your prospective hires the moment they walk into the door.
Of course, corporations would also no longer have any secrets - everyone would be aware of the dark dealings of major organizations, and prosecution of these organizations would be easy, since there'd be no way to hide what they're doing, and no way they could claim they didn't have the information about what they were doing.
This would also mean secret innovations would be worthless, since every company would know what every other company was doing, and copy it or improve upon it immediately to sell a better version. Small businesses would be especially screwed, since large businesses can copy anything they do and undercut the cost to drive them out of business.
The world at large would be a much more cautious, neurotic place, with every person focusing on their self-image (and the few that aren't being the dregs of society) while constantly worrying about government and criminals alike abusing their knowledge of their private lives. Everyone would be very polite to each other, while knowing all the dirty secrets of everyone at the same time.
In short, it would be a society of extreme paranoia.