Some planes are approved for Bluetooth (generally the ones with WiFi), others are not. Fewer are approved for cell signals (only the ones with inflight cell service)
I'm only going by the stuff I've read in the informational section of in-flight magazines [0]. I'm sure it depends on the regulatory environment of different countries, airlines and flights.
It used to be that running any uncertified electronic equipment at all was disallowed on takeoff/landing, no matter what the radio status. In the top hits on Google for "Portable IFE" I'm seeing WiFi devices on pages with 2012 copyright dates that claim no certification is required. Sounds like BS to me.
Well, I am going by the DO-178C/ED-12C (Software) and DO-254/ED-80 (Hardware) from the RTCA and EUROCAE which I have conveniently next to me since I am currently planning a Software Assurance Level D system for use in the A320.
Also I am going by the 2 Portable IFE systems from our hardware partners that I have in my Lab to play around with. Portable IFE systems are completely battery powered and have no connection to the Aircraft. The only "certification" that you need is that you would need to demonstrate that this device does not need certification. Which in the case of the 2 devices I have right here is fairly simple thing.