Tell please how to paint all vertices, not just visible, in vertex paint mode?
The only workaround I found is to use the Weights to Vertex Colors addon . It's not a real solution, just a workaround, but since you can paint through the mesh in weight paint mode by unchecking "Limit Selection to Visible" , you can paint there and then convert your weights into vertex colors. But of course it converts it in greyscale (although there's an option to use the rainbow ramp from the weight painting but that's not usable for most textures).
But I think a "Limit to Visible" option in Vertex Paint should definitely be added in Blender.
Set Vertex Colors (ShiftK) would do the trick.
Painting whole model in one color
Vertex paint mode select a color and press ShiftK
Painting a part of a model in one color
Edit mode select what needs to be painted with
Limit selection to visible button unchecked.
Vertex Paint mode press
Face selection masking for painting button, select color and use ShiftK to paint only selected vertices.