Virtually everything run by the government is to some extent botched. I can't think of a single department that is run properly, yet so many people claim the NSA knows everything. Sure they do.
You're missing the point and actually reinforcing the issue against the NSA: The NSA is already botching the whole damn thing - but WHAT they are botching is the fact that they alreday setup the infra to slurp all data. They farked up setting up controls that would prevent something like Snowden (thankfully) and what we are seeing is that they took IMMENSE technical power and are using it against everyone - the fact that they botched up the human aspect is, as you imply, inevitable. But they still have succeeded in getting the infra in place.
Certain agencies within the military run very well (JSOC and Army Corps of Engineers come to mind.) On the civilian side, NRC, OMB, NSF, Department of State. NSA under Alexander is also very well run after the post 9/11 binge abated.
The recovery efforts for Snowden are probably coming out of White House, DoD CSS, CIA, and FBI. Not wild about their performance here.