Lenovo T560 / T460 hardware compatibility
Solution 1:
I installed Ubuntu 15.10 on a Lenovo Thinkpad T460, and then upgraded it to 16.04. I've been using it for a few weeks, and these are the only problems I've hit:
When I upgraded from 15.10 to 16.04, Ubuntu started hanging whenever I move my mouse cursor off the HDMI external monitor onto the primary display. If I permanently remove the external monitor, then it everything is fine. This bug can be fixed if you manually upgrade to a newer kernel. This isn't as scary as it sounds, just a bunch of wgets then a "dpgk -i": http://linuxdaddy.com/blog/install-kernel-4-4-on-ubuntu/. Be sure to follow the correct 32 or 64 bit instructions on that page! More about this bug here Laptop freezes after connecting external monitor, since 16.04 update and here https://bugs.launchpad.net/ubuntu/+source/xorg/+bug/1559308.
The audio is sometimes slightly crackly, as if overloaded. It especially emits a crackle when the login screen displays and makes its quick bongo noise, as if the audio system has just been activated and isn't quite ready for business. I haven't noticed any problems while playing music though.
Twice in the month or so I've been using it, the wifi device has disappeared from Ubuntu's knowledge. Each time, after a few reboots, it reappeared again. Otherwise it's been rock solid. Who knows whether this is software or my hardware?
On 15.10, there was a bug which prevented long presses or drags when using the physical buttons of the trackpad. This has been fixed in the latest 16.04 updates (and maybe in 15.10 too, I don't know.)
Closing the lid would hang instead of suspend, but this problem has been fixed now.