A couple of thoughts:
Correct me if I'm wrong, but Kepler wasn't just looking for changes in brightness to indicate the presence of a planet, right? Because that only works if we just happen to be viewing the system edge-on, which would seem to narrow down the results rather significantly.
The other primary indicator for a planet is the "wobble" of the star itself in response to the gravitational effects of the planets around it. Our own star's barycenter is frequently outside of its physical radius thanks to Jupiter, this is something that would be visible from quite a distance away, and from practically any angle, not just edge-on.
My initial thought on KIC 8462852 is that we're seeing the transit of a brown dwarf, one that's a larger percentage of the size of the main star than we would otherwise expect. But, I would assume that a second star of that size would have a significant impact on the barycenter of the main star, and we would see a pronounced wobble that would line up with a large object performing a transit. In other words, they should have ruled out a second star by now. It also doesn't explain the odd timing of the transits... a single large object would pass at regular intervals, and we're not seeing that.
I didn't see anything on the star's wiki page about its barycenter, has it been measured? If not, given how many telescopes are pointed that way right now, hopefully we can get a measurement that should tell us a lot more about the structure of the system than we know now.
No, I don't think it's a Dyson Sphere. I'm in the camp that it's a natural phenomenon of some kind. If we do find out what it is, it'll be interesting to people that are into that sort of thing, like me (and presumably, everyone else in this thread), but will otherwise be somewhat underwhelming to everyone else.
As for the Fermi Paradox, it's my belief that we haven't seen anything because we're not really looking. Oh, sure, we're pointing our radio telescopes around, but even if the rather large assumption that aliens are using radios on the level of ours is true, most normal radio traffic barely leaves the system. By the time it reaches the next star, it's practically indistinguishable from background radiation, and that's only a few light years away. Yes, radio signals can travel those types of interstellar distances, but they have to be very high powered and very focused. Meaning someone would have to intentionally send a very particular type of radio signal directly at us in order for us to pick anything up. And we have to be looking at exactly the right spot in the sky at exactly the right time. And be looking for exactly the right type of radio signal, and it would have to fall within the frequencies that we're monitoring. That's a whole lot of "if"... maybe a bit too much to simply assume that we would have randomly "picked up something" by now. And also the rather large assumption that they're using radio at all. We've only had it for a hundred years or so.. it's a bit presumptuous to assume that everyone else is using it, and that even if they were, that the timing alone would happen to allow those signals to pass our way in the last, what... forty years or so? That's less than the blink of an eye in cosmic time.