As Ben points out In the case of nonplussed, the old meaning is "bewildered," while the new meaning is "unfazed". And with bemused, it's perhaps a more significant shift:
As the Visual Thesaurus wordmap for bemused indicates, the two primary meanings of bemused are "deeply absorbed in thought" or "perplexed by many conflicting situations or statements." The way that political reporters have used it about Obama, however, is "above it all, with a trace of amusement," in the words of New York Times deputy news editor Philip B. Corbett. Corbett adds, "but that's not what bemused means." Well, it's not what the word has historically meant, but the newer sense, influenced by amused, has become mainstream enough to enter some dictionaries, including Merriam-Webster's Collegiate.
"Skunked" seems like a good way of describing words that have two slightly different meanings for different groups of people at the same time. Perhaps they are words that are in the process of shifting from meaning 1 to meaning 2 but now just cause confusion because of this ongoing shift, and therefore should be avoided...like a skunk.
Of course, to loads of teenagers in the UK, the word "skunk" has totally different connotations (think "herbal" cigarettes and glazed expressions), so is that a "skunked" meaning itself?
Seeing language change actually happen in front of us is a fascinating thing and should be a reminder to us that language isn't about black and white but gradience. If you're an A level student revising for your Language Change exam, bear in mind that while we often teach you about periods of change (Early Modern English, Middle English etc.) the divides between these periods and the consistency of usage of a particular form at a particular time have never been that smooth. Above all, language is used by real - and often very different - people who don't all act or speak in the same way.