I upgraded from 39 to 40 and I think the only issues I had were:
Background I was using got removed, got a better one anyway
A few gnome extensions stopped working and I had to update them or find an alternative
Had to re-create virtual disk mapped to real disk for booting windows installation in virtual box (there is a sonicwall VPN I have to use for work which only works on Windows)
I think that was it!
I have had some strange behaviour from Firefox saying it's become unresponsive a few times and at the same time Thunderbird but that seems to have fixed itself now
Background I was using got removed, got a better one anyway
I had that happen a few times. This time I downloaded those backgrounds again (from gnome-backgrounds repository). Still, it's pretty annoying to have this happen.
I upgraded just before the beta. Discovered a mutter crash, reported it, it was fixed in a day or so.