On pages 144 and 145 you discuss how VDS,sat is not exactly 
VGS-VTHN. Why is the channel charge distribution, Q'I(y) not
exactly constant as you move away from the source? Why does
Q'I(y) become zero earlier at the drain?

When we increase the drain potential we attract electrons to 
the surface of the MOSFET and enhance the channel (this is 
drain induced barrier lowering, DIBL, discussed on page 154). 
This causes the channel charge distribution to become uneven
and lowers the value of VDS needed to saturate the device.