mosfet, shift registers grounding issues

In the present case it will be perfectly adequate just to jumper the two negative rails on the breadboard together. Returning multiple grounds to the Arduino is just what you do not want to do and you use only the nearest ground on the Arduino.

As MarkT has explained, the common ground point should be the MOSFET source pin and given that the lead between the breadboard negative rail and the actual source pin is very short and reasonably stout, that will work well on the breadboard.

On a PCB, you would have a large ground "land" adjacent to that source pin where all other ground points would return.