I'm a serious cyclist and runner who has a good "feel" for what my heart rate is based off perceived effort and decades of use of HRMs. So far my impression is that the Microsoft Band reads 10-20 BPM too high at moderate intensities. This is just an impression and not a controlled study or comparison.
That said, I wouldn't call it "extremely" inaccurate. What I consider "extremely" inaccurate is when my Garmins or Polars with a chest-strap would read 250 BPM, even when I was using silicone electrode gel. This would occur a few times on most of my bike rides and runs, perhaps due to the proximity of power lines.
In contrast, at least the Band seems consistent, if perhaps not as good at absolute accuracy.
Better, it doesn't constrict my breathing. I would almost never wear my HRM strap during a race due to such constriction, or that it would distract me by "riding" down my chest and produce inaccurate measurements.
In addition, it is wonderful not having to put on or take off a strap (and apply silicone electrode gel, or alternatively spit).
Finally, your HR is going to fluctuate from day to day for a given intensity due to weather conditions, how much you ate, and a lot of other variables. So I find that perceived effort is a better indicator of effort, and strictly use HR for giving me a snapshot on my training logs as to how hard I was riding or biking that day.
Because of all the above, so far I am liking the HR feature on the Microsoft Band a lot and am vastly preferring it to using a chest-strap.