Using Ubuntu MATE, the included /etc/default/grub, and grub2-themes-ubuntu-mate (as of 0.3.6~trusty4 and 0.3.6~utopic4), sometimes the only portion of the submenus (and edit dialog, etc.) that is visible appears directly beneath where the top level menu "box" was; the rest is obscured by the "border", and the content appears "cropped"; i.e., when I use the "Advanced options for Ubuntu" submenu, I probably won't see a menu of installed kernels, unless I have enough to appear within the visible area and/or my resolution is low enough. The applicable key controls are also invisible.
As a workaround, if I hit Esc to get back to the top level menu, and go back into "Advanced…" there is no obscuring border any longer.
This could be a bug with grub2 itself, and might apply to other themes; currently using 2.02~beta2-9ubuntu1 (trusty) and 2.02~beta2-15 (utopic); will see what happens with 2.02~beta2-18.
Note that update-grub warns that "Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported" for the default config file.