What is the most interesting grammar in Lojban?

The harder bits. 🙂 In particular:

* The fine differentiations in aspect and tense, including Lexical aspect (achievement, event, accomplishment, state). Hard to speak, not sure how successfully they’ve been taken up, but fascinating.
* The abstraction particles: Events, Qualities, Quantities, And Other Vague Words: On Lojban Abstraction. Even more fascinating, even harder to speak.
* Raising (linguistics) constructions, and the eye opener of how prevalent they are in natural languages: Events, Qualities, Quantities, And Other Vague Words: On Lojban Abstraction [tu’a, jai]
* The genuinely eccentric 🙂 approach to anaphora
* Like James Wood said, the open-ended case roles/prepositions, and their kaleidoscopic version of case grammar
* The argument structures of compounds (lujvo), which was more case grammar, and which I may have had a role in advocating: seljvajvo – La Lojban
* The text structure markers, which I found neat, at least in writing 🙂 Putting It All Together: Notes on the Structure of Lojban Texts

The attitudinals and tenses, actually, not so much: they were quite attention grabbing, so I didn’t find them as appealing. 🙂

The logical connectives were most useful to me in demonstrating how little  natural language connectives have to do with truth-conditional logic. 🙂 If is seldom translated successfully as ganai.