Did do-release-upgrade on my Ubuntu 16.04.5 LTS MATE virtual machine.
So it is Ubuntu 18.04.1 LTS MATE now.
And got the same error messages as you have.
Also there is no DropBox icon/indicator in the tray.
So I reported bug 1785622 to LaunchPad.
The solution is to remove one file
sudo rm /etc/X11/Xsession.d/99mate-environment
as it contain references to non-existent topmenu-gtk-module and then reboot.
Note: this file came from ubuntu-mate-default-settings package, it was replaced with newer version during upgrade to newer version. It has corresponding new file named /etc/X11/Xsession.d/80mate-environment for the same purpose.