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).
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."
The noises that the tribbles make were a combination of dove coos, screech owl cries and air escaping from balloons.
The pile of Tribbles near the end was actually created by gluing Tribble props around a large wire frame which William Shatner then stood in the middle of to give the illusion of mass numbers. In reality, there were only five hundred Tribbles made. This is obvious when you look at how the Tribbles are piled up, and none have landed on the floor at Spock's feet.