Why are there no nutrition facts on this US bottle of vinegar?
It may depend on the size of the label on the bottle - there are exceptions for small label area. Looking at a gallon bottle (different brand) that has the label, the numbers are all 0 anyway, which offers another option. If you happened to purchase it from a restaurant supply, that offers yet another exception.


  (j) The following foods are exempt from this section or are subject to special labeling requirements:
  
  (4) Foods that contain insignificant amounts of all of the nutrients and food components required to be included in the declaration of nutrition information under paragraph (c) of this section, Provided, That the food bears no nutrition claims or other nutrition information in any context on the label or in labeling or advertising. Claims or other nutrition information subject the food to the provisions of this section. An insignificant amount of a nutrient or food component shall be that amount that allows a declaration of zero in nutrition labeling, except that for total carbohydrate, dietary fiber, and protein, it shall be an amount that allows a declaration of “less than 1 gram.” Examples of foods that are exempt under this paragraph include coffee beans (whole or ground), tea leaves, plain unsweetened instant coffee and tea, condiment-type dehydrated vegetables, flavor extracts, and food colors.
  
  (13)(i) Foods in small packages that have a total surface area available to bear labeling of less than 12 square inches, Provided, That the labels for these foods bear no nutrition claims or other nutrition information in any context on the label or in labeling or advertising. Claims or other nutrition information subject the food to the provisions of this section. Foods in packages subject to requirements of paragraphs (j)(13)(ii)(A)(1) and (2) of this section do not require the information in paragraphs (d)(9) and (f)(5) related to the footnote, however the abbreviated footnote statement “% DV = % Daily Value” may be used.


Legalese from : http://www.ecfr.gov/cgi-bin/retrieveECFR?gp=1&amp;SID=4bf49f997b04dcacdfbd637db9aa5839&amp;ty=HTML&amp;h=L&amp;mc=true&amp;n=pt21.2.101&amp;r=PART#se21.2.101_19