Other mistake: When the robotic Ilya punches her way out of sick bay, the edges of the hole should be pointed outward, and there should be debris on the floor. There is no debris, and the edges are pointing inward.
Other mistake: When Kirk and Scotty are in the travel pod going to the Enterprise, one shot of the outside of the pod has them looking like two dimensional cut outs. Also, from interior to exterior shots of the pod Kirk goes from facing directly ahead, to a quarter profile and back.