Yes, but you are talking about history of ideas; this is not what is referred to by Zeitgeist, at least not by anyone who knows his German, philosophy, or history. The concept is philosophical and sociological, and it talks about the state of the world, of Life if you wish (or even Weltlauf in a way, if you want to use another Hegelian term), and that's what John's comment was aimed at, I believe: Mahler as an index of his times. Accordingly it is perfectly relevant to state things like (I'm not quoting directly) whoever doesn't hear the victorious forward march of the bourgeoisie in Beethoven's Eroica isn't really listening to it. In a similar fashion, in the case of Mahler and his music, Zeitgeist makes itself felt in the dissolution of the received sonata form, his Weltschmerz, etc. And it's not something that the composer needs to be conscious of at all; just the opposite, this is something that can only be understood in hindsight (ever heard of Minerva's owl?). At best, a person can become one with "Zeitgeist," expressing the historical movement, like Mahler; but it's not about some ideas residing in his head. The term as cultivated in popular parlance today refers to something completely different: it's usually about fashion, trends, signs of the times, that sort of things.
The challenge for source criticism that you mention applies to every existing historical record and is in no way limited to or more topical in the case of Bauer-Lechner's reports. In fact her notes form probably one of the more reliable Mahler testimonies we have whose veracity owes a lot not only to Bauer-Lechner's closeness to and respect of Mahler but also her unique ability to understand what the composer was after (in speaking as in writing, both personally and as a trained musician). In this sense I don't think we find many misrepresentations in the book and the questions you pose sound a bit academic and like something that appliy to any and all records of anything we ever take. I would tend to think Bauer-Lechner was herself capable of being critical already at the source to ensure that nothing less than the most truthful portrayal possible would emerge. If we are to try and gain a better insight into the very spheres inhabited by Mahler, I don't think we have a better place to start.
-PT