You are correct in thinking that there could be problems. Obviously, as you've stated, there is an offset voltage on the whole chip internal ground. Any analog inputs or outputs to external ground-referenced devices would require careful consideration.
In the case of the schematic snippet you have posted you would also need to consider what voltage each of the devices would see in the event of reverse polarity.
simulate this circuit – Schematic created using CircuitLab
Figure 1. The "protected" chip may not be all that well protected.
As shown in Figure 1, for example, D1 has prevented current being driven through the GND pin and backwards through the chip. 'IN', however, has no protection and some current may flow. Whether the chip survives that or not depends on the current and the internal structure of the chip.
A major plus is cost, because you can use multiple low current diodes, instead of one larger diode (or PMOS) on the input.
Careful here. You can't use diodes in parallel to increase current handling unless you take precautions (typically a little series resistor for each diode) to balance the currents through them.
My thoughts are that having an offset voltage which varies with current is not ideal.
Correct. If each chip had a separate diode they'd all be at different voltages.
I also remember reading that keeping an extremely low impedance path to ground helps to ground high-frequency noise which would reduce EMI.
Yes. You might get away with adding the capacitor to the chip + and - supply pins and leaving the diode out.