So, a cop Tasers a granny (one of thousands of such reports). It happened only a few miles from where I live, and I found it interesting to observe my own reactions to the event, and to see them change over time.
First, there was the inevitable, "Disgusting! Ridiculous! We are clearly living in a Police State!" 
My first reaction was essentially that the USA had finally managed to shed its last remaining shred of a legitimate claim to the title of "Land of the Free".
I was also filled with "Outraged of Tunbridge Wells"-style contempt for a so-called "man" who had to resort to such a weapon to subdue an old lady.
Next came a slightly dampened, "But, why am I so surprised?" Isn't this precisely what we should expect given the result of the 1960s' Milgram Experiment in which subjects of the experiment were induced by "authority" to give what they believed were painful electric shocks to other subjects. Milgram is quoted in Wikipedia:
"Stark authority was pitted against the subjects'
strongest moral imperatives against hurting others, and, with the
subjects' ears ringing with the screams of the victims,
authority won more often than not."
Read that after watching the video and listening to the li'l ol' lady screaming, and it's kinda chilling, no? But the point is, if Milgram is right, then the cop isn't necessarily a craven coward. Rather he's just one of the rest of us. Or maybe we're all craven cowards when it comes to it.
But finally, I attended to an increasingly loud alarm bell ringing in my head. One of my favourite cognitive biases (c'mon; everyone should have a favourite cognitive bias!) is the availability heuristic. 
This is simply a sciencey name for our tendency to overestimate the likelihood of something happening if we frequently hear about it happening. I alluded to it before in the context of bad economic news. And Dan Gilbert gave an entertaining Ted talk on the same subject. One of the points Gilbert makes is that the media (and I include in that all the rubbish we consume off the internet, like this blog wot u r reading) thrives on news that is big, and bad, and ideally both. And tasering -- especially of an old lady -- is, to most of us, bad. So we hear a lot about when it happens, and almost never when it doesn't. But the fact is, if the media is distorting our sense of reality when it comes to how often tasering happens, in the same way it distorts it when it comes to the threat of terrorism, then we really should work hard to maintain a sense of proportion.
Tasering old ladies is rarely going to be justifed. But I'll hazard a guess and say that most cops would agree; would share my initial outrage; would have kept their Tasers in their holsters and used common sense and some well-placed words instead; but as a result would never have made it into the news.