How accurate is Alcohol by Volume in beer? If I get a beer labelled 5% ABV, how accurate is that measurement likely to be?
tl;dr — By regulation, &plusmn;0.3-0.5%.

Chemically speaking, I'm not sure—maybe someone else can go into measuring techniques, alterations (continued fermentation?) during distribution, etc.

But countries and regions specify tolerances for error.

In the United States, according to Title 27: Alcohol, Tobacco, and Firearms, Part 7: Labeling and Advertising of Malt Beverages, §7.71:


  (c) Tolerances. (1) For malt beverages containing 0.5 percent or more alcohol by volume, a tolerance of 0.3 percent will be permitted, either above or below the stated percentage of alcohol. Any malt beverage which is labeled as containing 0.5 percent or more alcohol by volume may not contain less than 0.5 percent alcohol by volume, regardless of any tolerance.


http://www.ecfr.gov/cgi-bin/text-idx?SID=1affcd509f9614478fbbc0c85551765a&amp;node=27:1.0.1.1.5.8.41.1&amp;rgn=div8

In the EU,


  
  0.5% vol. for beers having an alcoholic strength not exceeding 5.5 % vol. and beverages classified under subheading 22.07 B II of the Common Customs Tariff and made from grapes
  1% vol. for beers having an alcoholic strength exceeding 5.5 % vol. and beverages classified under subheading 22.07 B I of the Common Customs Tariff and made from grapes; ciders, berries, fruit wines, and the like; beverages based on fermented honey
  1.5 % vol. for beverages containing macerated fruit or parts of plants
  0.3 % vol. for other beverages
  


http://www.icap.org/table/alcoholbeveragelabeling