Does your Mikrotik get its IP address via DHCP? In the IP->DHCP Client section, do you have an entry there? If so, check to see if you have "Use Peer DNS" set there. If so, any added DNS servers from IP->DNS will be overwritten by the ones passed out via DHCP. You will want to uncheck "Use Peer DNS" on that DHCP client entry so that you can specify your own DNS servers.
Ok I feel a little stupid but you guys did give me the idea of checking a pppoe client, which had been set up for 2 years now, and had "use peer DNS" enabled. It never mattered until a recent config change, although it should have never been set 2 years ago either.
This is on a dual core xeon x86 hardware.
Anyways there isnt even a place to go to /ip dhcp-client when you dont have the package installed at all, Ive never had it installed.