The Mac App Store noticeably experienced some problems last night / early this morning with downloaded apps. Upon opening affected apps, the system would say that the app is ‘damaged’ and cannot be opened, just like the examples from Graham. It certainly seems scary at first glance.
The error message recommends reinstalling your apps individually. While this will fix the problem, it’s a pain to do and isn’t necessary at all: your apps are fine, but the error message makes the situation sound far worse than it is. To simply fix the problem, just reboot your Mac, running OS X Yosemite or El Capitan, and the problem will ‘magically’ go away.
The more interesting question is, why did this happen at all?