My Sister, the Homemaker - S5-E12
Visible crew/equipment: At the beginning of the episode, Jeannie is talking on the phone by the stairs and her sister is hiding behind the banister. Her sister stands up for a moment and shows her full face, revealing that it is actually Barbara Eden's stand-in wearing the green costume.
The Night Dr. Loveless Died - S3-E4
Visible crew/equipment: The arm of the actual carriage driver is visible poking through the back of the carriage, slapping the horse and signaling it when to stop/proceed with a second set of reins, showing the actor in the carriage was not controlling the horse at all.
No Exchange on Damaged Merchandise - S1-E9
Visible crew/equipment: During the opening sequence, the bad guys' red Ford Galaxy reflects a bank of studio lights when the door is opened. (00:03:30)
That Old Gang of Mine - S3-E10
Visible crew/equipment: When the Turk is breaking into the palace, he pushes the window and it just swings open, since it is unlocked. However, you can see hands belonging to a crew member pulling the windows open to make way for the gag.
Carpetbagging, Anyone? - S2-E28
Visible crew/equipment: In the opening sequence, when troopers Stanley and Livingstone are heading towards the Captain's office, shadows of a production light and a boom mike and operator are seen on the ground.
Visible crew/equipment: When Will and Dr. Smith first come upon the Trader's encampment, just as the dogs start to attack you can see the head of a crew member (dog trainer?) bob in and out of view from directly behind where the dog on the right was lying...from behind the boxes stacked on the ship's platform. (00:08:38)