If you have a fixed money supply that is infinitely divisible, prices would be expected to fall due to deflation and increased purchasing power. Relative values of bread, hour of work, barrel of oil and a house should remain the same (with the caveat that their real values actually change - eg if we become an electric car economy then the relative price of oil in big macs will change). This makes no difference to anything of substance, it is just mathematics and psychology. The only real substantive issue is with debt repayments with deflationary currency, in which case I'd advise thinking hard about your loan terms.
I think your point about infinite divisibility is an interesting one. But the main downside is that there is no incentive to exchange the currency (a pizza or ownership in a business) when you know that the currency will be more in a year than it is worth today.
