A common example of a moving interface is an entire menu that moves as the controller does, eg. moving your mouse left makes the menu scroll to the right. Even a subtle effect like this can cause difficulty, literally trying to hit a moving target, with obvious consequences if a player has any difficulty with precision or timing.
While hitting a moving target is often a desirable challenge for gameplay, in UI it is generally not desirable. Particularly for games that are not based on fine motor skills, such as strategy, puzzle or quiz games.