The Enterprise Incident - S3-E2
Plot hole: In the conference room, Spock informs Kirk that his theory of a Romulan cloaking device kept the sensors from detecting the ships. However, in S1:E14, "Balance of Terror", they figured out the cloaking device, and how it worked. Unless he was feeding into the deception, Spock shouldn't have had any theory when it was a fact.
The Enterprise Incident - S3-E2
Plot hole: Despite the Romulan ships keeping a close watch on the Enterprise, when they beam the disguised Cpt Kirk over to the Romulan vessel it goes undetected.
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.