How about when Kirk's phaser falls off his belt when he's busting open Khan's freezer in Space Seed
? That always takes me out of the story for some reason. Deforest Kelley also noticed that it had fallen off, and briefly had a puzzled look on his face, probably waiting for the director to yell cut.
Scotty loses his accent in Doomsday Machine
when he says "Thirty seconds later, poof!"
In The Deadly Years
, Shatner appears to fumble a line: "I want everything in within about two minutes"