I used this textbook as an undergraduate before it was even a "book" at all -- just a bunch of packets handed out every few weeks. That was well over 10 years ago. Aozora was finally published as a textbook in 2003 or so, and it still makes a fundamental contribution to Japanese language pedagogy that few other texts can match. Most intermediate-advanced textbooks rely more on narrative passages than on dialogs, but the real core of Aozora is not the various short reading passages or "activities" sprinkled throughout the lesson units, but rather the many authentic dialogs, COMPLETE TRANSCRIPTIONS for which can be found in the back. In fact, there are nearly 50 pages worth of transcriptions! This is not common. Watching movies or listening to Japanese podcasts is fine, but the language learning benefits these activities confer are more limited than many students realize. After all, you probably don't have a written script on hand for your movie, so when a character says something that you just can't make out no matter how many times you rewind or repeat it, there's not much you can do other than ask a native speaker or a friend more fluent than you. Aozora brings these sort of "natural" conversations, with the little pauses, aizuchi, backtracking, confirming and repeating things -- in other words the way people really speak -- into the realm of the textbook.
But Aozora is not only about speaking/listening. The text is on par with any fourth-year level college textbook in its use of kanji, as well as in the sophistication of structural/grammatical patterns that appear in the dialogs. When I used it, it was in a course at the University of Oregon titled "fourth-year spoken Japanese," the focus of which was obviously on speaking and aural comprehension, but students' knowledge of kanji and grammar improved as well. Of course, it is NOT a replacement for grammatical reference works like Makino and Tsutsui's "Dictionary of Advanced Japanese Grammar" and "Dictionary of Intermediate Japanese Grammar," but then no advanced textbook is. Grammar is not what Aozora was designed to teach (at Oregon, the more formal training in grammar happened in the "fourth-year written Japanese" course, which used different materials).
If you are studying for N1 or N2 of the JLPT, the dialogs in Aozora will be helpful (I took and passed N1 some years after graduating, and I used Aozora, along with some JLPT prep materials, to brush up on listening).