Just did clean install of rel 2016-02-03 on 2 pi2s for my motorhome front and rear tvs.
Rear pi2 has wifi dongle and tethers an eth link to a pc and front pi2.
The rear pi2 tethers and its dhcp server assigns ip# and gateway# ok but fails
to assign a dns#. I plugged 8.8.8.8 on this pc and have proper internet access.
I am starting over with a clean install because it seems overnight last night
both front and rear pi2s ended up with blank screens and no way to talk to them.
They both had internet access so I think the no-dns# is new to 2016-02-03.
I tried some recovery steps but in the end it eemed easier to start over.
I think I’ve just run into a related issue. I too just did a fresh install of 2016-02-03 on my Pi 2 and had DHCP do its thing. Except it’s thing appears to be setting Primary DNS to 192.168.1.1, and secondary to nothing. Since the other dozen devices that use the same DHCP service from my router all have the correct values, I’m about 100% confident it’s not a problem with my router, which I just checked and found to be correctly setup. Clearly the DHCP client is not pulling the correct values from the DHCP server or at least is not plugging them into the correct settings on the OSMC install.
There is a known bug in connman where connman populates /etc/resolv.conf in reverse order to what the DHCP server specifies, which means if you have more than 3 DNS servers allocated the first DNS servers will not appear.
However if you only have between one and three DNS servers this would not affect you. (Other than the order being reversed)
Also keep in mind the GUI will only display the first two servers - which due to the bug above will actually be the last two that your DHCP server allocates.