I've been having eyeball issues, so this post may be more poorly edited than even my usual - and I'm not looking up links tonight, either.
I earn my living making and selling chemicals used in fracking wells, so I'm fairly familiar with what happens when they do that. I've followed a lot of what's been written on the environmental problems, including seismic ones, that are attributed to fracking, and I don't think of myself as overly biased. I have seen some really major messes that oilfield activities have caused, like the big treeless patch that was down near Smackover, Arkansas for most of the last century.
First, a very brief review of what a (modern) frac job is: it is the practice of pumping a lot of water (3,000,000 gallons +/-?) down the pipe in a newly drilled well with enough pressure (~8000 psi) and at enough rate (~3000 gallons/minute) to start a big crack in the hydrocarbon-laden rock at the bottom of the well. The water typically will contain less than about 0.5% of a selection of not-very-toxic chemicals (the ones my company sells) along with a lot of sand (a million pounds?) or a ceramic lookalike to sand. The chemicals are in there to reduce the pumping pressure and help carry the sand to bottom: the sand is there to get washed back into the big crack in the rock so that the crack doesn't close up again when they quit pumping. Instead, it "props" the fracture open so that the oil (or gas) that is in the rock can flow back to the pipe, out of the well, and end up as gasoline in your car. The pumping of the job might take a week or two, in four-hour episodes. The oil will continue to flow for a couple of years or more.
There don't seem to be any documented cases of earthquakes (of the feelable sort - very sensitive seismometers are sometimes used to measure how the fractures are forming) caused directly by a frac job. My take on this is that a piddly 3 or 10 million gallons just isn't enough to irritate Mother Earth into quivering. As others have pointed out above, though, you can inject enough fluid to promote whole swarms of little-ish quakes. The area near Prague, Oklahoma is a good example. If memory serves, they were disposing of maybe a million gallons per day of oilfield water into each of several wells there, and for months on end. The criteria for selecting the wells to put this into were almost certainly 1) proximity to wells producing water that needed to be gotten rid of 2) good mechanical integrity up near fresh-water zones, and 3) a bottom end in rock that wasn't a profitable source of oil but would accept disposed water if you pumped hard enough. Criterion 4), location away from subsurface faults that might fail with enough added water, was probably never considered at all.
Another example is a swarm of earthquakes near Youngstown, Ohio a few years back. The situation was similar, except that the water for their disposals came from Pennsylvania, where disposal wells were illegal. An immense amount of water was used to frac wells in Penn. It flowed back to surface with all the natural gas that the frac jobs freed up, and was wonderfully contaminated by all the salt that cohabited with the gas down in the Marcellus Shale. It couldn't go in the rivers, so it got loaded in railcars and sent to Youngstown. So at least there, fracking did actually cause quakes - one of 5+ magnitude, IIRC, but didn't do so directly. (My last trip through Youngstown was forty years ago, and at that time it looked as if being leveled by earthquakes might have been an improvement...)
The reason that water out of wells is typically reinjected deep into the earth is because it's too nasty to treat otherwise. The salt content, including table salt, calcium, magnesium, sometimes barium, and sometimes sulfates, make it largely impractical and uneconomical to purify. Even if you could distill it, all those salts would still need to be dealt with. You could take a lot of it to Smackover, Arkansas, and dump it on the ground like they did in 1915, but it would just make another big treeless patch there.
Solutions? There is a lot of work in our industry to find ways to reuse the salty "flowback" water on multiple frac jobs. More planning in where to drill disposal wells could help. This $50 per barrel oil price is having a chilling effect on the number of frac jobs being run, but I'm not personally to crazy about that solution...
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