Is it a faux pas to offer a favor to a professor who has written you a letter of recommendation / served as a reference?
This may vary greatly from person to person, but I, at least, would feel it was inappropriate to accept such a favor from somebody who I had written a recommendation for (unless it would already have been appropriate between us otherwise).

Personally, I feel that writing letters of recommendation for good people is not a favor, but a responsibility, a duty, and a privilege.  It is a responsibility and a duty because it is one of those little pieces of service that is vital to supporting the scientific endeavor and maintaining its quality.  It is a privilege because my opinions get to help shape the future of the field, and by supporting people who I believe in, I get to help make it the environment that I wish it to be.

In short: gratitude from a recommendee is appropriate.  Quid pro quo is not.  I would not hold it against somebody who offered a favor in return, but I would politely decline.

As I said, however, opinions on where the boundaries lie vary.  For example, I would not have requested information about web resources in the same email, as the professor did for you.  I personally think that is a faux pas (but, as noted, I'm pretty hard-line in my opinions here).  Thus, in responding, I don't think that you committed an error, though I would find the whole interchange a bit dubious myself.