It does work, but it's not usually the best option, and there may be some serious drawbacks. Many people swear by this method, but honestly, I've never been a huge fan. It works in a pinch, but I much prefer other methods of cleaning glass and mirrors.
The truth is, that the newsprint can smear on the glass, and more especially on the frame of mirrors and windows. Newspaper doesn't hold together very well, when wet. And given the opportunities to recycle newspaper that we have, it seems to make more sense to repurpose the paper instead of tossing it into the trash after wiping down a mirror.
Bottom Line:If you love using old newspaper to clean your glass and mirrors, then have at it...but there's probably an easier way.