Dear catch22:

On Saturday, March 2, 2013 10:16:46 AM UTC-7, catch22 wrote:
....
Would simply increasing the mass of the observed
objects account for the motions of those objects,

Yes, that could be made to work, but really special physics is required.

or must the extra invisible mass (dark matter) be
located in regions of space where there are no
visible objects?

That too. Understand though that we can see the dust that adds "flesh" to the bones of individual stars. But we cannot see the stars when they are too far away, they are point light sources, and we cannot image them. So distant stars without lit dust to add "size", are effectively Dark. Add highly ionized gas, that can only interact with X-rays or hotter, and you can have lots of invisible normal matter.

These two options seem to be mutually exclusive to me.

All a work in progress. Keep your hat on.

David A. Smith