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I brought a new Sony Xperia ZR about a month ago, I just recently happened to notice that the Bluetooth do not seem to connect/NOT even display any bluetooth device. Is there anything that I want to do on this new phone??
Before your phone can find another bluetooth device (for example a headset) the other device needs to be set to be discoverable mode or pairing mode. In order for another device to see your ZR you need to go to Settings -> Bluetooth -> [menu] -> Visibility timeout and select how long you want your phone to be visible over bluetooth.
If your phone can't find other devices even though they are set to be visible, try updating/repairing your phones software using PC Companion: http://www.sonymobile.com/global-en/tools/pc-companion/