We consider an optimal control problem subjected to a nonlinear PDE constraint such as the p-Laplace equation that serves as model problem in our numerical experiments. However, we are not primarily interested in the solution itself, but rather in multiple quantities of interest depending on the solution. Hence, we derive a posteriori error estimates for all functional at once using the dual weighted residual (DWR) method. This is done by combining all quantities of interest to one and applying the DWR method for this combined functional. These a posteriori error estimates are then used for mesh adaptivity. Finally, we substantiate our algorithmic development with numerical tests for the regularized p-Laplace equation. Additionally some recent results concerning iteration error estimates are presented.