The above picture, in which persecution is confused for prosecution, was featured in a recent episode of a sitcom aired on Fox Extended, “It’s Always Sunny in Philadelphia”.
To remind the reader about the distinction between the two, The Oxford Online Dictionary defines persecution as “hostility and ill-treatment, especially because of race or political or religious beliefs” (a common collocation would thus be religious persecution). The noun prosecution, on the other hand, refers to “the institution and conducting of legal proceedings against someone in respect of a criminal charge”.
The persecution/prosecution is just one among many commonly mistaken pairs of words, or “gruesome twosomes”. Others on this list include: affect/effect, lie/lay, accept/except, loose/lose, flaunt/flout, and, the here formerly discussed, healthy/healthful.
A BBC article reports that, sometimes, in spite of the best efforts in stopping the replacement of the two words, one of the words expands its semantic scope and enters common usage. Disinterested might be becoming synonymous with uninterested, and nauseous is replacing nauseated.
We will have to wait for a bit longer for a similar process to take place in our persecution/prosecution example. Mistaking persecution for prosecution, however, fits perfectly the mischievous gang of the Philadelphia-based sitcom.
I’ve frequently seen perspective for prospective, too. There are probably (perbably?) other per-/pro- pairs that get confused, presumably because some people pronounce the pro- with a reduced vowel, which comes out sounding like a syllable /r/.