relatively low DC voltages/current on a 2-sided PCB (say, 15V@3A max),
3A is not a low current, it can cause a lot of problems and is in the medium range.
've been confused by talk of 'isolation', which I assume refers to using mosfets, diodes, etc to ensure their positive voltages are isolated.
No that is not what isolation means. Isolation is the complete separation of both positive, negative and signals between two circuits. Isolation is not normally a circuit requirement. Don't confuse isolation with decoupling.
if I connected the shield to more than one arduino ground pin, would that potentially cause a loop
It depends, a ground loop is only a problem if large currents flow round it (greater than half an amp). This ha the effect of making the ground different potentials at different points.
Is it advisable to add a small resistor on the 0V DC connections from battery and DC supplies?
No in digital circuits it is a very bad idea. It is sometimes used on the output side of audio circuits where it is known as a round lift resistor. Even then it can cause trouble when interconnecting equipment.
is it good/bad/indifferent to connect the PCB's ground to the chassis (in one place only)?
it can be good, bad or indifferent depending on exactly what you are doing.