Not so bad as that, but it is a large area, and it's a challenge for optical astronomers to detect a faint source in such a large patch of sky. It's about the size of your two palms held at arms length. (Or, 40 times the size of the full moon, but that sounds less optimistic.)
The localization isn't performed through parallax, it's done through triangulation and time-of-arrival. For a pair of observatories, a difference in the arrival time of a signal (moving at the speed of light) defines a circle on the sky of possible source locations. With three observatories, there are three circles on the sky, which intersect at a single point.
The Virgo detector, outside of Pisa, is in the final stages of installing its advanced instrumentation. With LIGO+Virgo a source like the first detection, from September (a very loud event), could be localized to a patch of sky about 10 square degrees in area.
It sounds like you've already read about how we estimate the false-alarm rate for signals, so I'll just add that the estimated rate of BBH mergers was highly uncertain before this observation; the error bars spanned three orders of magnitude. See, for example, Fig 5 of http://arxiv.org/abs/1111.7314, which compares the previous LIGO-Virgo upper limits on similar events to the expected rate from population synthesis models and observations of high-mass X-ray binaries, known BNS systems, etc.
The rate inferred from GW150914 is on the high end of the rate estimates from astronomers, but it's completely consistent with prior observations. Certainly, if we had seen ten events in the first 16 days of data, it would not have made sense! But one event is well within expectations.
In Figs 6 and 7 of the second paper you can see the constraints from GW150914 on what are known as the "post-Newtonian" expansion terms of Newtonian gravity. Previously, terms beyond first order were only loosed bound, mostly from observations of the Double Pulsar system J0737-3039.
Just from this one event, we can also constrain the mass of the graviton to an order of magnitude less than the previous best measurement.
In addition to the two LIGO sites, there is the Virgo instrument outside of Pisa, Italy, which will come online later this year. The KAGRA detector is currently being assembled underneath a mountain in Japan. And, mentioned in another reply, LIGO has the equipment for a third detector. This is currently in storage in the hopes that the Indian government will build a facility. By 2023 there should be five widely-spaced detectors worldwide.
The resolution of time-of-flight between the two LIGO sites for the signal we just detected was about half a millisecond. This resolution is somewhat dependent on the signal strength and the location of the source relative to the detectors. With three sites we can localize most sources to tens of square degrees on the sky. This is still very large; the moon is a quarter of a square degree.
The odds are pretty good to observe only one event in 16 days of data, and the likelihood of seeing the event on the first day is the same as the likelihood as seeing it on the last day. The analysis of the remaining data from the first observing run (ended Jan 12th) will probably take a couple of months.
Another LIGO scientist here. It takes an overwhelming amount of energy to generate gravitational waves, and detecting them from terrestrial sources is about 20 orders of magnitude more difficult than the measurement we just made. Space, is extremely stiff; bending it enough to be detectable requires a huge amount of mass-energy.
LIGO scientist here. The way this is presented can be a little deceptive - the isolation is very frequency dependent. At high frequencies (>10Hz), the pendulums and blade springs in the suspension isolate the mirrors very well, so they are moving by only these small amplitudes (10^-19 meters). But at low frequencies (<1Hz) the isolation ratio is essentially 1, so the amplitude of the mirror motion is roughly the same as that of the ground (about 10^-6 meters).