On Wikipedia, is there a way to find out which edit introduced a specific portion of text?

Unfortunately, we don't have what programmers call a "blame" view -- where you can just press a button and see who's responsible for what in the current text. There is an experimental academic project called WikiTrust which does try to keep track of that sort of information, but that's just data that they gather along the way to highlight what parts of a page are trustworthy. http://www.wikitrust.net/

The surest way is to use the edit history.  Go back some arbitrary period of time (say, 1 year) and see if the text was there.  If not, try half a year.  Keep going until you narrow it down.  That should yield an answer via a number of steps proportionate to the log of the number of edits in the article history, although there are a couple things to watch out for.  Sometimes a controversial piece of text goes in and out of the article over time.  Also, sometimes it doesn't appear all at once but rather evolves as successive editors refine it. You can also sometimes find out what was going on by looking at the article's talk page (or for busy articles, searching the talk page archive).  Some things are the subject of a lot of discussion and debate, so if you want to know why a given article calls a certain person a "climate change denier" versus a "skeptic", or a particular historical person an "insurgent" versus a "terrorist", I'd look to the talk page first to find out why.  If you know when the edit was inserted, look to the talk page around that time.  If it's harder to figure out, just search for the term in the talk page.