The Paradigm Shift
The installation instructions for the 3.6.12 MediaVPs require you to place the new MediaVPs into FreeSpace 2/mediavps_3612. Previously, MediaVPs were required to be in "mediavps\". Thus, mods that come with a mod.ini that were released before August 6, 2010 presuppose you have the MediaVPs in "mediavps," leading to graphical glitches or the absence of MediaVP graphics in general.
Remedy
You have to edit the mod.ini to reflect the appropriate MediaVP folder. Double click on the mod.ini file (in / root) and look for the keyword: "secondarylist" (or find it with your bare eyes) and edit the folder name it points to, then save, in text only format.
For more information, check out the relevant articles on the FreeSpace Wiki!