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
The Enterprise crew are shocked to learn that their surprise capture may be due to a new cloaking technology possessed by the Romulans. Kirk and crew already encountered cloaked Romulans two years earlier in Star Trek: Balance of Terror
(1966). However, the cloaking technology in Star Trek: The Enterprise Incident
(1968) is new because it is improved. The Enterprise was still able to track a Romulan ship, though not accurately, in "Balance of Terror" and cannot detect them at all with this improved version. 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 ...