In the opening segment, in regard to the enemy vessels, Spock declares "Romulans now using Klingon design!" The actual reason for this was that in unpacking the models to shoot this sequence, a production assistant stepped on and broke the Romulan Warbird model that was going to be used, so they pulled out their Klingon Battlecruiser model and wrote the line to cover it up. See more
Transporter beams cannot penetrate shields, yet Kirk is able to beam to the Romulan flagship and back. This means that the Enterprise and the Romulan warships have their shields down, an unlikely scenario with hostile warships facing one another. See more
Enterprise Medical Log, stardate 5027.3, Dr. Leonard McCoy recording. I'm concerned about Captain Kirk. He shows indications of increasing tension and emotional stress.
I have completed the assignment, Captain: a theoretical incursion...
Captain James T. Kirk
Yes, Mr. Chekov, I can read, and as usual, your theoretical evaluations do not tally with mine. Return to your duty, and I'll let you know when your work is satisfactory. Mr. Spock, full sensor scan on the region, please.
I did give a ...