Mark Liberman cites this example fom the May 15, 2005 NYT article by Ian Fisher and Laurie Goodstein, "Pope Names American to Be Guardian of Church Doctrine."
Actingboth symbolically and consolidating his young rule, Benedict XVI announced today his first major public acts as pope: He named an American archbishop to be the guardian of church doctrine and he said he would speed up the process to make his popular predecessor, John Paul II, a saint.
My high school grammar teacher called this sort of thing "faulty parallelism." When my authors do it, I sigh, and move the "both" to in front of the participle—"Both acting symbolically and consolidating his young rule...." When my authors ask why I've done this, I explain that I wanted to make both parts of the sentence parallel.
Now I have another term to throw at my authors. Hooray!*
Of course, serious research into linguistic trends does not actually exist in order to provide me with jargon. The rest of the article provides a nice look at the way the usage is shifting. He notes, to my chagrin that "The pattern both DET [...] and [...] seems to be several times more common, across the board, than the pattern both DET [...] and DET [...]." So, "He had forgotten both his hat and mitts" would be more common than "He had forgotten both his hat and his mitts," even if the latter is, technically, more correct.
Best of all, even better than new jargon, though, is his conclusion about the NYT article:
I guess there's another possible explanation, besides language change in progress or a copy editor with delusions; perhaps this article, like The Dante Club, has slipped through some compositional wormhole from a parallel universe where linguistic norms are slightly different.
A compositional wormhole from a parallel universe would explain so very many things.
*Pace, Greg, if you are reading this. I deploy jargon only when strictly necessary to subdue people who won't accept the simple explanation.