I think it's interesting to talk about the failure of polls to predict the magnitude of the result. Here are the results of the final polls from six major polling organizations, taken 1-3 days before the vote

  Organization    Yes     No      Number*
  ---------------------------------------
  Opinium         0.479   0.521   1087
  ICM             0.477   0.523   1010
  Panelbase       0.474   0.526    954
  Survation       0.473   0.527    910
  YouGov          0.474   0.526   3043
  Ipsos Mori      0.474   0.526    951
  ---------------------------------------
  TOTAL           0.475   0.525   7955

  * excluding undecided voters

On one hand they were accurate in that they forecast a "no" result with high probability - the proportion of "no" voters is more than four standard errors away from 50%; the standard error being

  s.e. = sqrt(0.475 * 0.525 / 7955) = 0.006

On the other hand, the final proportion of "no" voters was 55.3%, which is more than four standard errors away from the forecast value of 52.5%.

So the polls were significantly underestimating the proportion of "no" voters out there. A similar effect was seen in the Quebec independence referendum, where the polls actually predicted a slight advantage for "yes" but the final result was a decisive victory for "no".