A couple of things to note (which I think you already have figured-out):
1. Dominants no longer necessarily point toward tonics- in some cases they might, but its not a certainty
2. Dominants might be respelled as augmented 6th chords- they also are likely to have 9ths affixed, or raised or lowered fifths
3. Modulations are brief and remotely-related
4. as was pointed out- the voice leading sometimes obscures the harmonic logic
5. tonics may appear in 6/4 position, which means that its harder to see the true tonic that is exerting influence over the chords around it
6. Look for modal borrowing; that means for instance, an f minor, or Ab major in C major.
7. as someone earlier said; listen for dominant to tonic resolutions (though in some cases they may be few and far between) and work backwards. You have to realize that in this literature, the tonal system as Mozart and Beethoven understood it, was coming apart.
Good luck though- its fun, and to me its very interesting literature. I like Mahler, Delius, Brahms, Korngold, Strauss....all of those guys. JS