Parallax demonstration (video clip)
The Quicktime movie below was created using a Nikon CoolPix 990 with the CoolPix fisheye converter in fisheye2 mode, and with a Kaidan Kiwi pano-head. The camera was mounted the furthest forwards possible on the pano head in order to accentuate parallax effects. Watch carefully and notice how the railings in the foreground seem to move relative to Buckingham Palace in the distance.
Note: the curves in the railings are caused by the fisheye lens and have nothing to do with parallax.
Correct use of a panoramic head, in particular the "lamp post test" will eliminate the parallax effects you see here.