Make sure that you don't use methds and properties introduced in later Office versions (2010 and later). Thus, you will be sure that your add-in will not fire exceptions at runtime.
The Running Solutions in Different Versions of Microsoft Office page states the following:
Solutions that were created by using Visual Studio 2013, Visual Studio 2012 or Visual Studio 2010 can run in Office 2013, Office 2010, or the 2007 Microsoft Office system. However, the solution can use only those features and APIs that are available in all three versions of Office.
BUT (and here comes the problem), on some machines it still requires version 12 although version 14 exists. Placing version 12 fixes the problem on these machines, but why does it happen???
The add-in shouldn't depend on the PIAs installed. You just need to include the required PIAs into the installer and use APIs available in the lowest Office version. That's all.