More relevantly to the discussion, this article about government spy planes and spy drones is interesting. It also describes the government's response following the San Bernardino shootings, and the drone flight paths over the mosque. Generally, I dislike BuzzFeed as too click-baity, but that's some cool interactive maps they show.
Despite terrorist attacks of religious nature seem to often come with multiple coordinated strikes, people seem to have an (understandable) aversion to the government monitoring mosques (invasion of privacy).
If one Christian goes and bombs a building, or shoots up a mall, I think it's due diligence to quickly check out their house/apartments and silently observe their church for a month or so, as long as personally identifiable information about members of the church isn't permanently stored for longer than, say, 90 days.
Or, if the Irish Republican Army was still heavily active, if one IRA member goes and firebombs a government building, and he frequented a specific bar, monitoring that bar for additional activities for a month or two for followup attacks wouldn't seem overboard.
So for me, the problem is more: How do we limit the duration so it doesn't stretch on for years, and how do we ensure the government disposes of collected information of innocent people after the due-diligence is finished? (And how do we prevent the government from distributing the information beyond the one task force that's investigating it, prior to deletion?)
I think short-term monitoring bars/mosques/churches/clubs that were attended by confirmed terrorists is justified, but I don't trust the government to delete the data when finished. It's kinda the "who will guard the guards" thing. Yea, we need the guards, but we also need protection from the guards.
Well given we can't just simply do nothing, but at the same time, let's not forget the amount of surveillance the NSA already does (Edward Snowden told us a good amount about this) , along with the Patriot Act (correct me if I'm wrong, but there are still portions of that active today, yes?). Monitoring bars/mosques/churches/clubs in the short term certainly makes sense. I believe that law enforcement is allowed to do so.
The problem really becomes when people start getting into the Islamophobia mindset and start giving the government more and more powers to do things that aren't really justifiable, and maybe target a subset of people more than others. Where does it stop then? When we can guarantee that terrorists won't attack? How much will it take to do that?
I have nothing against doing things within reason to stop terrorism/combat crime in general, but there is definitely a point that it is no longer just fighting terrorism but basically just mass surveillance based on a fear.