The Wikipedia article on the Gauss circle problem states that, if there are $N(r)$ lattice points of radius less than $r$ from the origin, then we know that $|E(r)|=|N(r)-\pi r^2|=O(r^{131/208})$.
Do we know whether this bound holds if we put the center of the circle at an arbitrary point in the plane rather than at a lattice point?