Visible crew/equipment: In the scene where Sulu flies the helicopter and accidentally turns on the windshield wiper, look closely at the bottom of the wiper and you can see the crewman's finger manually moving the wiper. (01:18:55)
Visible crew/equipment: In the scene where Mr. Chekhov is being interrogated on the USS Enterprise (the aircraft carrier) after being caught on board, a studio microphone being used for the shot is visible hanging above him. (01:14:45)
Visible crew/equipment: During the scene on the bus, two members of the camera crew are visible in the window behind and to the right of Spock. The crewman of the left is sitting and operating the movie camera, and the crewman on the right is taking still camera shots. (00:43:50)
Visible crew/equipment: During a close up of the police officer's sunglasses, when Chekhov is asking for directions to Alameda, some crew are visible in the left lens. They are a line of people trying to stay out of the camera. (00:43:30)
Visible crew/equipment: At approximately 01:32:50 on the Blu-Ray, you can see a diver releasing the mechanical whales. He is on the far right side of the screen, you can make out his head, body and left hand. He is visible for a good 8-9 seconds. If you have a different media source, it's during the Bird of Prey decent. You see a closeup of Kirk, followed by a closeup of Uhura and Gillian, then a close up looking down on the harpoon. It's in the following scene. (01:32:50)
Answer: They only give him a schematic of the molecule. The man even says, "It would take years to decipher the matrix", or something like that.