Bluetooth Connection
I have had the same problem, where starting my Bluetooth devices no longer sync up automatically with my phone. To make these devices work, you have to go to your Bluetooth settings and scroll down to the connected devices, then manually connect the device that you want to connect to. This is very inconvenient, since I have to do it each time that I get in my car. This is not a problem that I had on my Nexus One.
The other Bluetooth issue that I am facing is that when I am connected and listening to audio-books using the Audible app (and I have heard the same problem exists for streaming music), the connection goes in and out many times while I am listening. Also, many times when the screen is turned off, I lose the Bluetooth stream completely, but it returns immediately when I click the power button to turn my screen back on. It seems like there is some sort of "sleep mode" that is disabling the Bluetooth connection when the screen is powered off. My trick for this is to leave the device plugged in, with the 'stay awake when charging' setting enabled on the phone, this way it never goes to sleep therefore disconnecting me.
I absolutely love this phone, but these Bluetooth connectivity issues are very annoying.