Does sour-cream go bad?
Eventually, yes...  but it does have a fairly long shelf life.

According to Eat by date, you should expect 1 to 2 weeks after the date on the package.  They say:


  You can tell if sour cream has gone bad if you notice dark mold on
  its surface, bright bacterial marks, pockets of watery liquid and a
  sharp, bitter flavor. First the liquid will begin to separate, at
  which point it can still be used but within a week you will need to
  throw it out when you notice mold on the inside of the lid and then in
  the product.