When Stiller leaves the cabin to go after Eva, the gun he is carrying is not the bolt action rifle he loaded earlier - it's a pump action and the front ring sight is missing. The scope has also been reversed and it barely attached as it flops around as he fires, and it falls off shortly thereafter. (But if all of this is not "real" then is is really a Goof?)
One shot is fired at a car, yet three bullet holes are then seen in the windscreen (2hr 50m).
In the second part of the film, the scene at Fred's cabin: When the camera moves surrounds the cabin, at one point the shadow of the camera is clearly projected on the wooden wall.
In the beginning of Part 1 around the 7:10 mark as the camera does a long pull away from Professor Vollmer and Lause, a crewman's (possibly the camera operator) shoe can be seen reflected in the mirrored pedestal with the bust on top of it in the right hand bottom corner of the screen.
When Stiller drops Eva off at her home and then goes in after her after a change of heart he goes into the living room looking for her, then he runs into the swimming pool area. As the camera pans to follow him around the pool you see the reflection of a camera man in the glass at the middle right of the screen.