I’ve routinely found the standard Adobe Flash player updater for Mac (OS X/macOS) fails right at the end, without explanation.
However there is a version that always works. Go to:
… and choose Flash player for Safari and Firefox – NPAPI – the download URL is normally:
The opening dialog box should look a bit different – like this:
Use this version (last tested 10 Feb 2017):
Firefox plugin checker
This is a very fast and handy way of seeing if your copy of Flash or Silverlight is up to date.