Just to say, it’s now August 2016, and this problem is still alive and kicking (it wasn’t just a problem with one specific build of VS2015).
For me, I ended up having to install VS2015 on a train, and using up my entire mobile phone’s 2Gb monthly data allowance, as although it claimed only one package was corrupted, it ended up re-acquiring everything.
Oh, and then it got stuck whilst trying to install the packages. Giving up on the install, and rebooting my laptop actually got it started again.
So, short answer: the VS2015 installer still isn’t particularly stable.