Most all of this has already been said, but whatever i agree wtih it:
Search function, and with that either AH system or organisation to the market wards.
Non laggy menus. Seriously how can you play the game when u can't control it enjoyably and have to slow down your own inputs?
A little bit more incentive to party, and reasons to use regimens.
Inventory sort, map markers.
Equipment wear more readily visible instead of selecting it in the inventory menu.
Target distance as has been said, similar to the plugin for XI. I always found it invaluable for avoiding aggro in tight spaces.
A recipe book as others have said, though not necessarily just select the recipe and it inputs the ingredients for you. I'd be happy just with being able to look up ingredients from the menu in game instead of tabbing out (which can't be done full screen anyway) and looking at a website. Should also have a way to readily look at the so called "learned" recipes from doing guildleves and quests anyway.
Auto jumping up small ledges, as in FFXIII. Would hate manual jumping and ending up with attention whore morons constantly bunny hopping all over.
Chat dividers as ppl have said, tell/LS/etc. Also a larger chat window or a way to temporarily make it full screen like in XI. Hell just enlarging it in general. Maybe this is already implemented but i can't figure out how to do it.
Fix the extreme delays with buy/sell menus at shops. Maybe that's just a beta thing. But also, don't show my currently equipped gear in a sell list, or at least grey it out and skip over it when scrolling. Maybe even some kind of divider here like the chat divider to show weapons/armor/etc. Make it all more intuitive and a faster process.
Similar to gear divider above, only show gear that can be equipped in the current slot i've chosen when equiping gear.
A more detailed check system for mobs, and maybe adjust mob lvl distribution/consistency and/or positions.
Less confirmations as others have said, less clunky UI. Using an elevator should actually save me time as opposed to running down the stairs.
And finally probably only a beta thing, but a little more direction/explanation/tutorials. And variation on leves.
Someone mentioned more voice acting in some cutscenes, i just don't see that happening due to the nature of MMOs. They can be adding new shit for years and if it's a recurring character the chances of them being able to get the same voice actor again and again seems fairly slim to me. And I'd rather not end up with different voices for the same NPC, so i actually hope they don't add any more voices because of the potential to screw things up in the future. Frankly i was surprised there was any voice acting in there at all.
Oh god how could i forget: MAP ZOOM, faster pan