Commenter Nick Carr makes an excellent point, which, if you'll forgive me, I will copy-and-paste:

While I think there is, at a mechanical level, a clear parallel between the two practices, at an intellectual level they could hardly be more different. Commonplacing was a means of more deeply internalizing an author's words, as its early practitioners often pointed out. It was a sign of attentiveness, of profound engagement with text. The cutting and pasting, or mashing up, that we do online today tends to be much more cursory and superficial.

I have a "commonplace book", though I didn't know to call it that – a notebook where I hand-copy interesting passages from books I'm reading. Perhaps I'll start doing the same with passages from the web, as an intentional slowing-down of the process of textual palimpsest generation...