I've seen a few circuits where forward biased diodes are used in series from some point in the circuit to ground to get a small reference voltage equal to voltage drop across diodes below ground, for example in LM35DZ's datasheet. Is this applicable here? Where else it would work and where not?
It is applicable but is has some problems.
The voltage you are dropping on the diodes times the current will be dissipated as heat, and you have to provide an higher voltage transformer to account for that drop or have a lower output with the same transformer.
Also, a diode does not switch on cleanly at 0.7V, meaning that at a light load they will drop less than 0.7V and with high loads (1 A +) they can drop as much as 1V. Diodes also exhibit something called a "dynamic resistance" which you can understand as a small value resistor in series with the diode.
As you can see on this graph, the voltage drop on the diode varies with the current passing trough it (although by a small value):
If you want some precision on your supply you shouldn't mess with the ground path, thats why Dave put the current sense resitor on the high side with a differential amplifier instead of putting it on the ground return.