The scene in which Kirk is buried in an avalanche of tribbles took eight takes to get right. The tribbles were thrown into the hatch by members of the production crew. The crew members were not sure when to stop because they were unable to see the scene. This is why additional tribbles keep falling on Kirk one by one. William Shatner can be seen looking perplexed as to why more tribbles keep falling on him.
To create the one tribble moving on its own, the prop supervisor bought a battery powered toy dog and stripped it down to the mechanical works. Once recovered with fur including the toy legs, the prop moved on camera along the railing on the Enterprise bridge without wires or external assistance. The toy was so noisy all the dialogue in the scene had to be looped with ADR (re-recorded after shooting).
The noises that the tribbles make were a combination of dove coos, screech owl cries and air escaping from balloons.
William Shatner recalled the great enjoyment all the cast had filming this episode. He noted, "The trouble we had with 'Tribbles' was [to] keep your straight face. It was just a lot of fun."
During the famous "bar fight", careful observers will note that while tables are broken, all the chairs remain intact. The tables were studio property: the chairs were rented, and if damaged would have to be paid for.