Visible crew/equipment: Right as Young Biff starts to chase after Marty through the tunnel, there is a shot of the wheel spinning around, and you can see the camera crew reflected in the hubcap. (01:29:45)
Visible crew/equipment: During Bud and Coffey's fight in the lab, we see a lightbulb swinging from side to side between the two men. If you look closely, you can see a hand (belonging to a third person) pushing the lightbulb. The only people in the room are Bud and Coffey. (01:44:16)
Visible crew/equipment: In the elevator shaft/rocket boot sequence, the 'arm' of the lift device that is actually holding Spock casts a strong shadow on the wall to our right of Spock, indicating the arm goes from Spock's back to the black vertical slot in the right wall. It is most visible as Spock first lowers into view next to Kirk. (01:02:40)
Visible crew/equipment: When the girl falls to the ground in the warehouse, the safety mat she falls on is visible.
Visible crew/equipment: When the chairs are flying through the air in the courtroom, if you look closely, you can see the string pulling one of them. (00:34:30)
Suggested correction: This would need more clarification. I couldn't see any string in the mentioned sequences - and for the record, I don't think strings were used, you can easily find interviews with the production team that mention the different trick at work here (they quite literally 'shot' the chairs up in the air).
Visible crew/equipment: When Toxie walks into the video store and discovers that a gang is destroying it he grabs one of the gang members and punches him in the stomach. If you look at the guy's belly just before Toxie punches him you'll be able to see a big red spot on his shirt. This big red spot is actually the blood pack that the guy is wearing underneath his shirt and also where Toxie is supposed to hit him.
Visible crew/equipment: Martin Brundle (in fly form) manages to kill a guard by spewing acid vomit all over him. Right after this happens he roars and you can see what looks like a colander (probably used to increase the spread of the vomit) in his mouth.
Visible crew/equipment: At the beginning of the movie, when the two assassins get out of the car, you can see crew members (filming from a low angle for Blade's POV) reflected in the car door as it opens. (00:04:47)
Visible crew/equipment: When the neighbours visit the Szalinskis to get their baseball and Nick opens the door, you can see the reflection of the cameras and lights in the glass.