Suppose you use bayesian filtering on the text surrounding the links to determine whether the connection is good or bad. With a reasonable amount of data it should be possible.
Note: I'm not an algorithms guy, I do business and strategy and a wee bit of programming, so maybe the example isn't good, but I thinkthe point is.
That's how I'd solve this particular problem though. As I said in the parent I only have cursory experience in programming, and almost none in algorithms.
http://oreilly.com/catalog/9780596529321
Naive Bayesian classifiers are just one of the more popular types; others include Support Vector Machines (SVMs), decision trees (and their relatives, random forests), and a bunch more. If you'd like to play around with some, Weka is good open source software for this:
Determining sentiment (the topic of the NYT piece) is considerably harder though, because it would allow for spammers to write negative articles about a site and link to it and negatively affect its rankings. Also, determining the tone/emotions of a piece of text is probably one of the hardest things to do with textual analysis
This could be solved by making sentiments act as a weight (i.e. a multiplier in [0, 1]). Positive sentiments would give a particular reference more weight, negative sentiments would give little to no weight. Then it would be impossible to negatively affect a site's rankings - only positively affect them. Just like now.
As for determining sentiment, it's not something I've ever tried to do, but is it really that hard ? Intuitively I would think positive and negative articles would have significantly different distributions of certain words.