I'm just going to wait for the first lawsuit that hits the city.. of which there will be many.
First there is that right to privacy, which they are clearly violating. Demanding information that would normally require a warrant of some kind is going to hurt them badly.
And eventually the first person who has their identity stolen, which includes pretty much anyone the employee interacts with via social network sites, will take the city to the cleaners. It doesn't matter if the city managers claim they didn't poke around where they weren't supposed to, they simply won't be able to prove they weren't the person that divulged the information to someone who could take advantage of it.
As for email, that's fast becoming as protected as postal mail and if you have access to a person's Google account you have access to their email.
Again it really doesn't matter what the employees actually look up, the city has created a liability for themselves by demanding their employees hand over this information. They become liable for every employee who has access to this information.
We all know how well threats to employees about being fired or prosecuted works when it comes to not looking up things they shouldn't.
I work for a State Department and regularly see new employees turned out the door with a promise of further action when they're caught poking around places they shouldn't.
For example, anyone who has computer access at the Child Support department will eventually have a friend ask if they can "look up my case". Just accessing that information if you are not working on the case is an instant dismissal and very likely to end in a court appearance. But they still do it and many are even stupid enough to try to "help" their friend by making favourable alterations.
So promises of "we won't do that honest" are worthless, and when something goes wrong every employee or friend of that employee has a very wealthy target to sue whether it was the City's fault or not.
Obviously only an idiot would work for this city, but it might be worth applying for a job and then refusing to sign the disclosure paperwork just for the financial reward if you know a decent lawyer.
Of course as everyone knows in the US, this is how millionaires are made. It's amazing how often some business or public entity volunteers to be the means to enriching Americans. The level of stupidity employed here is actually a pretty good example of how it happens and however overplayed you think the attitude that most Americans are thick as two short planks, I'm sorry but actually they really are. They usually have about as much awareness of the consequences of a given action as your average dog.. which is to say none at all.