Sulu falls out of his chair, but at the very next change of camera angle (an overhead shot of the entire bridge) he is seen still sitting in his chair.
At 12:37, Kirk and Spock watch a Klingon ship on their view screens. Not only is the vessel flying backwards, it moves out of frame of one view-screen and onto another that is supposed to display the same image.
The sensors are not reliable ("in chaos" says Spock), then they see a Klingon ship, which fires on the Enterprise. The Enterprise returns fire with phasers and the Klingon ship vanishes. Spock says the Klingon's shields clearly deflected the phasers, nor did it cloak to disappear. He then reaffirms that the sensors are still not registering normally. If the sensors weren't working properly, Spock would have no way of knowing any of this.
Captain Kirk gives the first star date as 52.2. That would chronologically put this adventure ahead of quite a lot of other Star Trek shows (except maybe Star Trek: Enterprise (2001)). Approximately two days later, he gives the star date as 5267.6, which makes more sense.