Background The specification must be a Color specification or Automatic:
Graphics3D[{Arrow[{{0,0,0},{1,0,1},{0,-1,0},{1,1,1}}]}, Background -> Red]
Notice that opacity cannot be specified by passing a List containing Opacity together with a color specification like {Red, Opacity[.1]}. Use a color directive with an alpha channel instead:
Plot[{Sin[x], Cos[x], x / 3}, {x, -Pi, Pi}, Background -> RGBColor[0.5, .5, .5, 0.1]]