The reason for jagged shadows lies in the technique used for rendering the shadows. I assume you used the blender internal render engine and the standard shadow of the lamp; for spots lamps the default is the buffered shadow.
Here is a rough explanation how buffer shadows are calculated
With buffer shadows something like a render is made from the view of the light source lamp. Every surface point not visible on this lamp-rendered image isn't reachable by this light source. Thus, these pixels of the lamp-rendered image projected to the unreachable surfaces will be a good approximation of the shadow in the final render. According to this the blockyness depends on the resolution of this lamp-rendered image. It can be adjusted at the lamp settings:
Here is more info on how the buffering works.
So increasing the size is the solution?
I hope your shadow pass is blockless with this method now :)