Have objective and verified tests been done of the effects of personal electronic devices on a commercial airliner's operation? Have any governmental agencies done comprehensive tests on the effects of personal electronic devices used in the cabins (and cockpits) of commercial airliners?  

With the ubiquitousness of cell phones, laptops, kindles, ipads, etc, it strikes me that everyone seems to just know that using a cell phone in the cabin of an airliner has no appreciable/measurable affect on the electronics of the aircraft.
Yes, they have done a lot of testing, hence why they now finally realize that most electronics are of no harm, and you can use them.

The FAA announcement page has a link to a fact sheet of their report, as well as a link to the PDF of the report.

In addition to the FAA report, other agencies have weighed in (such as Boeing).  Basically, the rules were instituted in the 1960s, and remained virtually unchanged since then, so it was time to make a change.