Shore Leave - S1-E16
Revealing mistake: There is a wooden or straw hut - some kind of man-made structure - visible in the lower-left of the frame behind Kirk and Bones as they walk. (00:12:30)
Shore Leave - S1-E16
Revealing mistake: Stock footage turns the single plane strafing Rodriguez and Angela into two attacking planes for a moment. It becomes one plane again when it flies over Kirk and company. (00:33:40)
Shore Leave - S1-E16
Revealing mistake: After Rodriguez and Angela run from the strafing plane, they end up stopping next to a tree. Angela falls to the ground without Rodriguez knowing that she was hit by the gunfire. He continues to watch the plane disappear with his head looking upwards. When his head comes back down, rather than looking towards her to talk (where her face would be if she was standing), his eyes immediately look down at her on the ground...as if he'd been expecting that she'd be lying there all along. (00:34:01)
Shore Leave - S1-E16
Revealing mistake: Near the end of the episode, the heavy chains restraining the "loose" tiger are visible both around his neck and running across the rocks to the right of the shot. (00:42:35)
Shore Leave - S1-E16
Revealing mistake: When Yeoman Barrow places her tunic on a shrub while changing, automobiles can be seen in the background through the brush.
Shore Leave - S1-E16
Revealing mistake: During the scene with Sulu and the samurai, each actor casts three shadows. Plus as the samurai rushes Sulu, the "sky" appears black behind him.
Suggested correction: They're on a planet where their every thought can be almost instantly created in physical form. Within the context of the episode it wouldn't be unusual to see literally anything in the background. Perhaps one of them was thinking about something involving that structure and it was being constructed for them.