I don't like using var in that way, because it seems like you're declaring two distinct variables. In your example, I'd much prefer:

   function make_dot_product(dim) {
      var dot;
      if (dim === 3) {
         dot = function(a, b) {
            return a.x * b.x + a.y * b.y + a.z * b.z;
         };
      } else if (dim === 2) {
         dot = function(a, b) {
            return a.x * b.x + a.y * b.y;
         };
      }

      return dot;
   }

This also makes it clearer what happens if neither dim is neither 2 nor 3.