In the first scene during the Kobayashi Maru simulation watch the wall to Savik's right when she is in command. There is a white piece of paper oddly taped to the wall there. It shows up about 3 times during the battle scene. When the simulation is over, however, and Kirk is addressing Savik on the simulated bridge, you can see that where the piece of paper was taped there is now a symbol. The letter "A" is above the symbol (you can see the bottom of the "A" during the battle but the rest of the symbol is under the piece of paper). That paper must have been a stencil that had the white paint applied to it but was not taken down before shooting the first part of the scene. Maybe the paint wasn't quite dry. Oops!