
Plot hole: The assassin cuts a hole in the glass to kill the Federation president. But with the size of the hole and the placement of the scope on the phaser rifle, the assassin would not have been able to see out of the hole.
Grumpy ScotPlot hole: At the end Sulu knew where the secret meeting was but didn't think to notify Enterprise, knowing full well what the situation was with the ship and Kirk etc.
Suggested correction: Sulu didn't know about the bird of prey that could fire when cloaked, so didn't know the importance of them getting there.