Sometimes yes, sometimes no.
Bill Cosby has been arrested for sexual assault. On the other hand, that was a very long arc.
•Ethan Couch, the rich kid who killed four people while drunk driving (the affluenza case) has been busted violating probation. Though apparently the most he’s likely to get is 120 days.
•A 12-year-old boy gets shot by cops because they reacted to his toy pistol. They won’t be prosecuted but people in authority are very concerned that protesters and black activists not lose their tempers about it.
•Some members are outraged about NSA spying on Americans … well, as long as they’re the Americans in question.
•One Netflix documentary on a murder case has inspired protests about the conviction … on Yelp.
•In 2012, a SWAT team in Kansas burst into a residential home looking for drug dealers—because the father had bought hydroponics equipment at a garden store (the cops watched the store and marked people who did that). A judge has thrown the family’s case against the cops out on the grounds the police clearly didn’t do anything wrong.
•Health care providers routinely violate medical privacy laws without penalty. At the link, the government explains its priority is breaches affecting more than 500 people, not just one or two.
•On the other hand, an alleged scam artist targeting charities with office supply offers (for example sending unsolicited supplies, then harassing the mark for payment) has had its accounts frozen by the federal government.
•A musician has sued Spotify on the grounds streaming services (which pay shit to the artists they stream) don’t get the necessary licensing from songwriters. Billboard has more details.
•Tennessee has charged a woman with murder for attempting to abort her child. I guess as the right-wing slides ever more extreme, any pretense they care about the women in these cases is over.
•Right-wing casino millionaire Sheldon Adelson buys a paper and by a Complete Coincidence reporters start investigating the judge in a lawsuit against Adelson. One Connecticut reporter (the story wound up in a Connecticut paper) resigned over management’s shamelessly delivering what Adelson apparently wanted. More details about the tissue of lies and fictitious reporter Edward Clarkin at Think Progress
Fraser Sherman's Blog 
None of these stories has to do with the “arc of the universe”, just stuff humans get up to. The arc of universal justice would be things like if we destabilize the weather enough, we make the planet uninhabitable for people, and cockroaches get to rule the Earth. Or we attract sufficient negative attention from an extraterrestrial civilization that they go “enough” and vaporize us. News stories are generally negative by definition, because nobody wants to read about the happy valley where nothing went wrong.
I was thinking of that quote of MLK’s, that “the arc of the moral universe is long, but it tends toward justice.”
Thanks for the reminder! It’s still hyperbole, but it now has an improved pedigree by association.