When an observer is in motion, from side to side or vertically, distant objects will seem to move much slower than nearby objects. This is due to the distortion of length due to perspective.
Some neurological research suggests that motion parallax gives more depth-perception information than our binocular vision does,note thus a one-eyed person can still determine distance quite well, if he moves his head a bit.
Thus, any truck or pedestal movement will reveal depth information not available to the single eye of the camera. It can call into question, very quickly, the flatness of a painted backdrop, either on set or in animation.
Live action shows with windows on the set (and sufficient budgets) will often build the landscape outside as several layers of flat cutouts, thus giving some motion parallax to the background. This same idea was used to create pseudo-3D backgrounds for computer games during the 16-bit era, when computers and consoles didn't have the horsepower for proper, textured 3D. A common bragging point on the boxes of many games is the number of simultaneously composited scrolling parallax layers the game displays at once.
To get around this problem in animation, some use multiple background cel layers, moving at different speeds. (In the past this has required a special piece of equipment called a "multiplane camera" - see the extras on Disney's Bambi DVD for details - but the effect has become much easier to manage in the digital age.) Excessively cheap animation (see Filmation, Hanna-Barbera) uses the single Wraparound Background, and this intensifies the fakeness.