The Witch Doctor's Big Bad Voodoo can be runed to Rain Dance (The ritual restores 122 Mana per second while standing in the ritual area.). Does this extra effect of Big Bad Voodoo affect other classes in any hidden way? And if not, does it affect a 2nd Witch Doctor if there is one in the group, or only the caster?
The effect for the aura of Big Bad Voodoo works for your entire party. However, the Rain Dance rune specifically restores only mana. As such it will ONLY work for Witch Doctors but WILL work for allied Witch Doctors as well. Allies that aren't Witch Doctors will still gain all effects of the aura (including the mana regeneration), but since they don't use mana that part of the effect will do nothing for them.
The description of the rune is specific to restoring Mana, so it won't restore anything else. It will, however, restore mana for other Witch doctors as well.