Visible crew/equipment: After starting their four day journey through the long dark of Moria, a few shots later Gandalf pulls on his hat brim, and just as he walks (with Legolas close behind) to his left (towards the viewer's right), up some stairs, the black electrical cable leading from the staff to under the robe's left sleeve is visible. (00:19:30)
Visible crew/equipment: When the fellowship are in the tomb they spot the orcs coming so they lock the doors. When it does a close up from the outside you can see the shadow of the camera on the bottom left of the left door. (00:28:20)
Visible crew/equipment: After Gandalf removes the One Ring from the fire and places it in Frodo's hand. The large overhead set light is reflected in the Ring, above Frodo's reflection, as he turns it between his fingers in the second close-up of the Ring. (00:37:20)
Visible crew/equipment: During their fight at Orthanc, in the wide overhead shot, as Saruman flies backwards towards the large doors, the wire attached to the back of Christopher Lee's outfit is visibly pulling his clothes. (00:50:45)
Visible crew/equipment: When Saruman points both staffs at Gandalf, he says, "I gave you the chance of aiding me willingly, but you have elected the way of pain!" as Gandalf spins round on the floor, with his left leg raised in the air. As he spins, there is a bulge at his side and the apparatus with the wire, around his left ankle, is perfectly visible. (00:50:55)
Visible crew/equipment: After Frodo looks into the mirror and sees the destruction of the Shire, Galadriel is seen riding in the swan boat across the river. Look in the background, on the left bank, a man can been seen sitting there, very faintly. As the scene progresses this crew member can be seen looking back and forth. (01:01:50)
Visible crew/equipment: After Boromir picks up the Ring, while he's admiring it you can see the camera reflected in it.
Answer: It is a different staff. Look at the branches at the top of the staff.
Garlonuss ★