can they also copy anything suspicious in "plain view", like whatever is brought by a simple search on the hacked Exchange? That is one huge dragnet. Of course any good citizen wouldn't mind when a law enforcement would come take a look around after the crooks have already broken into the place.

Edit: to the iudqnolq's reply below - warrant doesn't have to explicitly permit it. My understanding [IANAL] is that, at least in the physical world, whatever gets in "plain view" of the officer during any authorized law enforcement activity also becomes a fair game. I.e. they were called for the noise and upon entering see a kilo of heroin laying on the table - the heroin comes into play even though they didn't have a search warrant for it. So i'd expect that the same principle would be applicable in the virtual world too.