Shadow quality on objects varies wildly as camera moves

I need help with shadows.

On the left, a nice clean shadow.

On the right, the same object now exhibiting a jaggy shadow + a pattern of pixel dots on the unshadowed area.

No change in settings - this happens just from tilting the camera view a little. I’ve set everything to the very highest quality.

1443626--77656--$2shadows.jpg1443626--77656--$2shadows.jpg

1443626--77654--$Shadow Res.png

Nobody?

I would really appreciate any help on this. You can see this object has sharp shadows from one angle, and distorted / glitchy shadows when viewed from another. Where does the problem lie?