Plum is an adjective meaning desirable, and it also denotes the sweet, purplish fruit. The adjectival meaning originated as a figurative extension of the fruit. Plumb is a verb meaning (1) to determine the depth of, to probe, or (2) to work as a plumber; an adjective/adverb meaning (3) exactly vertical, (4) utterly, or (5) squarely; and a noun meaning (6) a weight on the end of a line, used to determine water depth. Writers commonly confuse the two homophones in all their meanings.
Examples
These writers use the adjective plum correctly:
Urban Meyer is joining ESPN as an analyst less than two months after he surprised the college football world by resigning from his plum job as Florida’s coach. [The Canadian Press]
When James K. Polk won the presidency in 1844, he named Buchanan secretary of state — a plum appointment … [Salon]
Palin notified CPAC organizers Thursday morning that she wouldn’t accept the plum slot as the conference’s keynote speaker next Saturday night. [The Hill]
And these writers use plumb well:
Though plumb in the centre of Europe, Budapest, for me, always casts a hypnotic east-meets-west spell, thanks to its years under Ottoman rule. [Telegraph]
Major American corporations employ a multitude of psychological and scientific analytical tools to plumb the hearts and minds of customers. [Seeking Alpha]
Or maybe these people are just plumb out of their minds. [Southern Chester County Weeklies]

