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Rendering CG-scenes with motion-blur results in longer rendering-times. Furthermore it's a lot harder to composite several elements together when they're already blurred. The usual way to deal with this, is rendering a separate "velocity"-pass of each frame (and each element... like background, foreground, individual objects...), which stores a velocity and a direction for every pixel in the frame. This allows the image to be blurred accordingly AFTER being composited.
If you don't have a velocity pass, there's still the possibility of using "motion compensated motion-blur" (there are several plugins out there doing this, and since version 7 it's included in the Pro version of AfterEffects as well), which analyzes the motion in the frame, and blurs the image based on this. Problematic areas are fast moving parts (where the difference between one frame and another is to big to be regarded as "motion"), or areas on the image's edges (where objects suddenly enter the frame, without the plugin knowing, where it was the frame before). And these "problem areas" usually cause the artifacts above.
