So what elements would most often be cut out (and which TAS episodes still depict such, but briefly)? Based on the answers above:
* Romance ("The Survivor" managed to have one anyway)
* Duplicated scenes
* Drawn out song and dance ("The Lorelei Signal" did have Scotty's Welsh ditty)
* Extraneous description
I think the deciding factor depends upon if its integral to the story.
For “The Enterprise Incident”, Spock’s romance story with the Romulan Commander would be central to the story. And no one would know that Kirk is alive and disguised as a Romulan until near the end of the story; his “death” would only be alluded to in the teaser. Which would save a lot of time.
Whereas for "The Gamesters of Triskelion", the romance between Kirk and Shahna is not integral to the story at all, and would be cut.