Visible crew/equipment: When Kane is struggling on the table shortly before the alien rips through his chest, just before the first patch of blood appears, his T-shirt rides up and something strapped to his chest can be seen. This is some sort of pack containing fake blood that discharges onto his T-shirt. (Best viewed in slow motion.) (00:55:40)
Visible crew/equipment: Following the chest-burster scene, as the camera pans around the darkened corridors on the Nostromo just prior to Dallas ejecting Kane's body, what appears to be a boom mic is visible only for approximately two seconds to the left of the screen. (00:57:10)
Visible crew/equipment: When Ripley is heading towards the Shuttle towards the end, just before she finds Jonesy, there is a POV shot where the camera is walking towards a ladder. If you look at the floor you can see the dolly that the camera moves on. (01:36:05)
Visible crew/equipment: When Ripley is in the escape pod and has the space suit on, she hits the button to open the door and blow the alien into space. In the shot just as the alien is getting sucked backwards, you can see the wire coming out of its back. (01:51:30)
Visible crew/equipment: After Ripley fails to shut off the auto destruct sequence, she runs through a corridor filled with gas. As she exits from the gas right before the shot cuts away we see her pass by a full sized light. Beside this light is the clear arm and head of a lighting crew member. (This is acknowledged on the DVD commentary).
Visible crew/equipment: As the Alien drops down behind Brett (before it kills him), you can see wires attached to the Alien's back.
Answer: According to the commentary on the DVD, Ridley didn't add this scene to the original cinematic release because he thought it revealed the true horror of the Alien too soon in the film. The scene is quite early in the film and he thought revealing the fully matured Alien at that time would reduce the viewer's fear.
I had watched Alien several times before I noticed the Alien hanging there.At this point the Audience have no idea what the Alien looks like, they're looking at pieces of science fiction equipment put in by the production crew that they can't relate to, so for all they know the Alien could just be a piece of kit hanging there.