Shadow maps have an advantage, being an image space technique, that they can be used to shadow any object that can be rendered. You do not have to find the silhouette edge of the shadowing object, or clip the object being shadowed. This is similar to the argument made for depth buffering vs. an object-based hidden surface removal technique, such as depth sort.
The same image space drawbacks are also true. Since the shadow map is point sampled, then mapped onto objects from an entirely different point of view, aliasing artifacts are a problem. When the texture is mapped, the shape of the original shadow texel does not necessarily map cleanly to the pixel. Two major types of artifacts result from these problems; aliased shadow edges, and self-shadowing ``shadow acne'' effects.
These effects ca not be fixed by simply averaging shadow map texel values.
These values encode distances. They must be compared against r values, and
generate a Boolean result. Averaging the texel values results in
distance values that are simply incorrect. What needs to be blended are the
Boolean results of the 
and texel comparison. The SGIX_shadow extension
does this, blending four adjacent comparison results to produce an alpha
value. Other techniques can be used to suppress aliasing artifacts:
/texel comparisons can then be averaged to
smooth out shadow edges.
values are biased by a
small amount. Making the values a little smaller is equivalent to moving
the objects a little closer to the light. This prevents sampling errors
from causing a curved surface to shadow itself. This biasing can also
be done with polygon offset.
One more problem with shadow maps should be noted. It is difficult to use the shadow map technique to cast shadows from a light surrounded by objects. This is because the shadow map is created by rendering the entire scene from the light's point of view. It's not always possible to come up with a transform to do this, depending on the geometric relationship between the light and the objects in the scene.