Microphone Support
The built-in microphone has not worked since 4.8, although Pulse detects an input device.
Is there some alsa configuration or channel that I'm missing for this to work?
I was able to get mine working by running alsamixer -c 0 then pressing F4 and raising the 'Mic' value (mine was at 0 initially).
Mine was at 100 when I followed the same steps:

Do you see the levels changing when running pavucontrol and looking at the 'Input Devices' tab?
No. alsamixer values have no affect on pavucontrol values it seems, and the bdw-rt5677 mic does not detect input signal in pavu

Odd, yeah my panel shows two entries for bdwrt5677.

I imagine our systems differ significantly though because I'm running Arch w/o any desktop environment (but with pulseaudio). Wish I could help more -- microphone issues plagued me for a long time with this machine!
I am running Ubuntu 16.10 too and I can't get the mic to work. No amount of fiddling with alsamixer seems to help.
Wanted to bump this thread. I'm having the same issue. Is there any addition info I could provide that might help find a solution?
edit to provide a bit more info: Looks like I'm having a slightly different issue. My headphone mic shows unplugged.
I actually managed to get the Mic working after a reinstall. Make sure you have /etc/modprobe.d/sound.conf in place, reboot, then run the audio scripts (several times to be sure).
If you've migrated from a kernel before 4.8 then I'm not sure what will make it work.