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Wong (1978, 2002, Foundations of Paul Samuelson's Revealed Preference Theory), repeatedly refers to "Pareto’s proof of the immeasurability of utility". What was this proof?

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I think the "immeasurability of utility" refers to what we know today as the non-uniqueness of utility representation. The word "utility" also has a slightly different meaning there. As Pareto notes in the mathematical appendix to his 1909 book, Manual of Political Economy (limited preview on Google Books), the "utility" measure is

the measure of pleasure provided by the combination [of quantities of consumption goods], or [...] the measure of the value in use, the utility, the rareté (Walras), the ophelimity of this consumption.

He goes on to prove that there is a lack of a one-to-one correspondence between quantities of consumption and the indices of indifference curves (which are the candidate for measuring utility). Therefore he concludes that indifference curves are merely the index of utility (i.e. pleasure), not the measure of it.

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