Microsoft SQL Server 2012 RS Add-In for SharePoint fails to install.

You are trying to install the Reporting Services add-in for SharePoint Products
https://msdn.microsoft.com/en-us/library/gg426282.aspx 

This fails and you check the logs @ C:\Users\<your user>\AppData\Local\Temp\RS_SP_<a number>.log

What you see is something like this:

...

Total number of configuration settings run: 2
Total number of successful configuration settings: 1
Total number of unsuccessful configuration settings: 1
Successfully stopped the configuration of SharePoint Products.
Configuration of SharePoint Products failed.  Configuration must be performed before you use SharePoint Products.  For further details, see the diagnostic log located at C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\15\LOGS\PSCDiagnostics_3_3_2015_16_51_12_997_108052037.log and the application event log.

2015-03-03 16:51:35:
2015-03-03 16:51:35: Install error: C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\15\bin\psconfig.exe return error code: -1
2015-03-03 16:51:35: Error details: System.Exception: C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\15\bin\psconfig.exe return error code: -1
   at RSCustomAction.BaseProcessLaunch.LaunchCommand(String fileName, String arguments, Boolean ignoreExitCode)
   at RSCustomAction.PsconfigCommands.CopyAppBinContents()
   at RSCustomAction.RSFeatureSetup.Install(Boolean repair, Int32 addRetries)
2015-03-03 16:51:35: Uninstalling Report Server feature.
2015-03-03 16:51:35: Stopping W3SVC service.

...

I do not know why but this error is caused by having comments in one or more of your web.config files.
So, the solution is remove any comments in the web.config files and rerun the installer.

Web.config files are here: C:\inetpub\wwwroot\wss\VirtualDirectories\<port number>

Comments are surrounded by <!-- -->

So, for example:

<!-- this is a comment-->