There are a hundred small details I could mention, but here are the more general issues I've found hard:
1, Word order: subject-object-verb, and putting prepositional phrases, adverbials, etc. between the subject and the predicate.
2. Informal vs. Formal Persian: really extreme differences at times!
3. The subjunctive, especially the perfect subjunctive.
4. Obviously the writing takes a long time to get use to, but you do eventually become accustomed to it. To me it seems easy since I went through the horrors of learning Chinese writing :-P
But even when you add the harakat short vowels, it's hard to guess when a و is an "o" or an "u". Also, the "hidden tashdid" in Persian is annoying (eg جدی)
5. EZAFE!!!!!
On a technical note, typing from right to left sometimes makes my computer go insane, but that's a software issue, not a language one.