The world has changed rapidly with the advent of the web and desktop publishing, so it's going to be difficult to say what is customary. You will probably find that there are generational differences as well as differences between fields and institutions. For example, what is customary at MIT is for professors to put their course materials in OpenCourseware.
It's always been common for a set of lecture notes to be written down, then polished over the years, and eventually transformed into a textbook. That means that the distinction between a textbook and a set of lecture notes has always been fuzzy. However, I think the amount of fuzziness has increased recently, because publication in print no longer has to mark the threshold. Many people go through the whole process of evolution on the web, with no involvement from an editor or the traditional publishing industry.
But to the extent that the distinction between free online lecture notes and a free online textbook is detectable, detecting it may help you to guess what is the most polite and constructive approach.
If it's really a complete, standalone book, then the author has put a lot of effort into making it into a polished product, and will definitely be grateful to hear that the effort is paying off, and that you and your students are using it. With traditional books, the author always knows how many sales s/he's made; with a free online book, s/he doesn't know unless the users take the trouble to make contact.
If it's really a set of lecture notes, then it may be less polished and self-contained. The author may feel that its unfinished state doesn't reflect as well on him/her as he/she would like professionally, and may have only put the notes online with the intention of making them available to his/her own students.
As the author of some free online physics textbooks, I find it a nuisance that there are so many outdated versions of the books sitting on the web. The most recent version is the best and reflects the best on me. For this reason, I'd suggest not mirroring people's notes on your own server, even if they have a Creative Commons license that permits that. If you're concerned that they'll evaporate off of the author's server, just keep a private copy as insurance against that eventuality.
I have a hard time believing that anyone who has posted lecture notes online will be upset that a student studying them prints them out so s/he can read them, highlight them, etc. However, I think many people would be more sensitive about a situation where the notes are being reproduced and sold in a campus bookstore or at a copy shop. Sometimes they'll state their expectations explicitly on the web page. If they choose an explicit license such as a Creative Commons license, then just make sure you don't violate the license.
Solutions to problems can be a sticky point. E.g., if you're thinking of distributing solutions to your students, I would discuss this with the author of the problems. Distributing solutions on paper may be more acceptable than distributing them electronically.