I have been developing and building my add in on a machine with 10.2.1 and installing and running the add in on machines with 10.2.0. It works for me. Not sure if it makes a difference but the add in project was originally created on a machine running 10.2.0 before being upgraded to 10.2.1. Also, the ESRI references in the project are set to specific version = false. Now, building on 10.2.x and running on a machine with 10.1.x is another story, that does not work. And in the hopes of saving someone like myself some time, if you need to build a 10.2.x add in project on a 10.1 machine go into the csproj file with a text editor and change (MSBuildExtensionsPath)\ESRI\ESRI.ArcGIS.AddIns.11.targets to (MSBuildExtensionsPath)\ESRI\ESRI.ArcGIS.AddIns.targets