How bad is this broken brake cable strand? I just bought a new bicycle. While I was fiddling with things (removing tags, mounting a light, etc.) I noticed that the boot on the rear brake cable was loose. When trying to reseat it, I found that one of the strands of the brake cable was broken, and poking through the boot. Furthermore, the cable is un-twisted just before the bolt that clamps it to the right side of the brake. These seem like very bad things to me which I should immediately get fixed (and complain about). Am I correct? Is the bike unsafe to ride?
I wouldn't say that a single broken strand on a new brake cable would render the bike "totally unsafe to ride," but if it is an option you should bring it back to the shop and have them replace it. This might be a sign that whoever put this bike together or inspected it for sale doesn't have a very thorough shop ethic. If they were careless enough to install a brake cable incorrectly, there may be other - more serious - oversights which can add up rather unpredictably. Not totally unsafe, but not ideal for a new bike.

In any case, brake cables are cheap and should be replaced at regular intervals.