There is a custom build version (2016.2.824) that use latest extensions. Upgrade to this version using the UI (as shown on the attached screenshot). Then perform following actions to install the extentions:
Navigate to "C:\Program Files (x86)\Telerik\Test Studio\Browser Extensions\Firefox4+" and drag telerik_test_studio_automation-2016.2.823.0-fx-windows.xpi to a Firefox window.
Navigate to "C:\Program Files (x86)\Telerik\Test Studio\Bin\TestRecorderBrowserExtensions\Firefox" and drop telerik_test_studio_recorder-2016.2.823.0-fx-windows.xpi to a Firefox window.
Here you can find more info about the extension troubleshooting.