This is a nifty little neologism, and here is Rosenthal's piece (link to: http://www.nytimes.com/2009/09/27/magazine/27FOB-onlanguage-t.html?_r=1), which offers numerous useful examples. Among them: enervated, which means "weakened," not "energized," and fortuitous, which means "by chance," not "fortunately." Rosenthal cites seven others: fulsome, noisome, enormity, disinterested, penultimate, presently and restive.
Some of these words are misused all the time, to the point that they have almost begun to mean what they sound like, which seems to be the primary difficulty with keeping their true definitions in mind. It's hard to fight Usage City Hall, and if enough people get hold of a word and give it the wrong meaning, ultimately that's what the word will mean.
It's been my experience that copy editors have trouble with these words, too, primarily because many of them are such assiduous readers, and have at their disposal a continually replenished supply of verbal erudition (I might have said verbiage there, but that one means "wordiness," and all I meant was "many words," a neutral use). The peril grows when you're editing quickly, and I often find myself at those times looking up words for which I think I'm certain of the meaning; it slows me down before I do something dumb, and also reacquaints me with the tools of this craft, sort of as if I were a surgeon checking to make sure I had the right knives for the procedure.
Except for verbiage, which I have often heard used neutrally, the only other example of a phantonym I could think of really isn't one: inflammable. According to my Merriam-Webster, it means the same thing as flammable, but it's the older word by more than two centuries, first appearing in 1605. By the time flammable appears in 1813, common use must have found the "in" particle suggestive of "not," as in inadequate, so flammable came to be.
I found Rosenthal's little piece on phantonyms useful, but I'm still trying to think of other examples. If you've got one, leave a comment below.