Not exactly covered in the other post, which didn't involve interisland flights.
The regulations have recently been changed, and limits increased. You can now take up to two bottles of wine and two liters of hard alcohol per person. http://www.tahiti-tourisme.com/plann...iticustoms.asp
There are no TSA-type liquid restrictions on the interisland flights, so you can carry-on your duty-free bag from LAX. But be aware of the weight limit on Air Tahiti -- 6.6 pounds (3 kilos) -- if over that, you might want to pack your duty-free liquor in your checked luggage (well-wrapped). I've heard rumblings that they are now weighing all carry-on, which wasn't common in the past. Free checked luggage on Air Tahiti is limited to 44 pounds (20 kilos) per person (not per bag), but the overweight fees are not terrible if you exceed that. http://www.airtahiti.com/faq.php?cat=Baggage#56