How long would it take to scan the visible universe for unique signals? The article Amazing rays as star succumbs to dark side talks about a very large black hole swallowing up a star. The report goes on to say that the only reason it was discovered was because it shot out a signal directly at our Solar System, by chance. 
A discovery that was 3.8 billion years in the making, as our Solar System spins around and happened to collide with that signal at the right moment in time. Given that the universe is around 14 billion years old and this was only 3.8 billion years ago (the Earth may not have existed when this event occurred). But I digress.
This discovery implies to me that it's very hard to even detect significant events. That is, we have to be pointing our listening equipment at very minute areas of the sky to detect an astronomical event.
So even with our available array of detection hardware here on Earth as well as orbital telescopes, how much of the visible sky have we already scanned? And how long will it be until we've "scanned" the universe?
To help clarify the question, I know that there may be areas of the sky that may be completely void, so perhaps scanning "the relevant universe" is a more appropriate scope of this question, but if you can guestimate the whole visible sky, it would be interesting to know.
 A: There was significant luck involved with this detection to be sure, but it doesn't involve either the figure of 3.8 billion years, or with happening to have our instruments pointed in the right direction. We were lucky that Earth happened to be sitting directly in the path of a very narrow beam of radiation emitted by this event. The third image on the page shows an artist's depiction of what the beam might look like if you happened to be very nearby and a little to the side of the beam.
As a matter of fact, there is a great collaboration of x-ray and gamma ray astronomers all over the world in attempting to scan the entire sky [EDIT: in the high energy bands of x-rays and gamma rays, at relatively low resolution], continuously. Very high energy events called gamma ray bursts, somewhat similar to this one though obviously not identical, are detected regularly, but last for only a brief time. The collaborators have automatic notification systems in place so that telescopes capable of viewing these events can emergency slew to the sky position to view them before they disappear.
NASA's Swift spacecraft is one of the leading early warning systems, and the Chandra X-ray Observatory and Fermi Gamma-ray Space Telescope are leading follow-up observing platforms.
http://heasarc.nasa.gov/docs/swift/swiftsc.html
http://en.wikipedia.org/wiki/Chandra_X-ray_Observatory
http://fermi.gsfc.nasa.gov/
That this event was observed at a distance of 3.8 billion years gives us a (very crude!) estimate of how rare they are- We have had the capability of detecting these events for 10 or 20 years, tops, so these events apparently occur once per 10 or 20 years per spherical volume of space 3.8 billion light-years in radius. Don't get too attached to that number, though, because any professional reading this will totally be grinding his teeth, reminding me that you can't do any kind of reliable statistical extrapolation from just a single event. So... very crude indeed. Caveat emptor.
[EDIT: To clarify, what we call an "event" must include not just "black hole eats a star" but also "black hole eats a star and the resulting beam points directly at Earth". If we assume that the beam is about 1 degree wide, narrow enough that it is therefore only visible to roughly 1/10,000 of all possible directions, then the bare black-hole-eats-star event would have to occur 10,000 times as often for one to happen to point at us.]
A: Sky surveys have been made for millenia, with whatever technology was available at the time (eyeballs to start with).
At this point, the entire sky has been imaged at least on photographic plates, and there is modern imaging for a large fraction of it from surveys like 2MASS, SDSS, and many more. (Wikipedia, of course, has a list, far from complete). Such efforts are indeed highly scientifically productive, and more are planned (DES, LSST, and more). 
Each survey only covers limited wavelengths, has a limited resolution, and only sees to a limited depth (brightness), and only at a limited set of times. So, none of them sees anything remotely close to everything that it would be interesting to see.
Even when we put significant effort into surveying a small area of with nothing specific of obvious interest, as was done with the HUDF, we find plenty of scientific interest.
So, to answer the question, it isn't clear that we have scanned any of the universe to the limit of what could be useful. Particularly when you consider wanting to, say, record the evolving spectra (from radio to gamma ray) of transient events, the task is effectively arbitrarily large.
A: What a timely question! We just spent a week at STScI hosting a conference on the topic of wide-field surveys, and very roughly speaking, there are four fundamental characteristics of any major survey: 
wavelength (radio, IR, X-ray, etc)
field of view (e.g. 10,000 sq degrees)
depth ("R band to 26th magnitude")
cadence (revisit each spot of the sky every X [hours/days/months])
For your specific example of tidal disruptions by black holes, Pan STARRS expects to see tens of events per year, while LSST will see hundreds or even thousands. But there is a HUGE software problem of processing so much data. One speaker this week pointed out that LSST will generate a list of ~100,000 events of interest every night. To maximize the benefit of so much data, we really need to improve the way we sip from the fire hose.
