Same bluetooth problems, but different symptoms. I haven't seen anybody with these issues yet:
Before update to iOS 7.1, bluetooth worked fine in my car on the handsfree ('09 Infiniti G37x).
After update, whenever my phone wakes up due to an email, text, anything that is enough of an event to wake the screen up, my car goes into handsfree mode like the phone is going to say something (as it would if Siri were trying to communicate w/ me over bluetooth), but the phone won't "hang up" the car stereo until I hit the sleep/wake button on the top of the phone. At that point, it "drops" the car audio.
So something like this happens: Email comes in, phone dings, screen wakes up, stereo interrupts music as phone connects to it, nothing comes over the audio from the phone. I see the option to "hang up" on the car display, but hitting that doesn't break the connection. Only after hitting the "sleep" button on the top of the phone does the connection break and the car audio come back on.
I believe that if I wait long enough and the phone screen powers down itself, the connection will break then.
Weirdest thing, but easily reproducable for me.