I've linked direct to 0V and haven't had any problems but the potential for problems is there. It's not just badly written code which could make an input into an output but an adverse external effect, from lightning strike nearby to EMI from other machinary.
If a resistor is used you are protected from the inputs becoming ouputs, shorted to 0V then it is possible those pins and thus the chip can be damaged. This should not happen and rarely does, but can.
A convenient, and small footprint solution is to use SIL resistor packs for pull-downs alongside the DIL socket, cut the resistor pins off for PICAXE pins which do not need to be pulled sown.
Another potential disadvantage to tying Serial In to 0V is that it can never be programmed in-circuit. With a pull-down resistor it can be, though it is more complicated than attaching the 22K/10K resistor serial interface.