Guesses and/or notes, based on the few short clips in the video. Not necessarily in order:
Ifrit Extreme:
- Tons of nails to down.
- Lots of Ifrit Cyclones at the same time.
- Small and difficult to reach safe spots for Radiant Plumes.
Garuda Extreme:
- Adds much stronger, possibly up most of the fight.
- Nowhere safe to stand during tornadoes, party needs to keep moving the whole time.
Titan Extreme:
- Titan-Egis.
- Multiple rock jails at once.
- Mountain Buster looks like it hits almost the whole arena.
- Bombs/8-way landslide/plumes all-at-the-same-time madness.
- Some kind of large stomp move that knocks everyone off the arena if it's not stopped in time.
Ultima Weapon:
- I loved this fight in the story, looking forward to the new hard mode.
Crystal Tower:
- Sounds like just the first "floor" (Labyrinth of the Ancients)
- The 3 party groups split up for certain encounters, join together for main bosses.
- FF III boss music.
- A way to fight Behemoth with a small group and not just insane amounts of lag.
Thornmarch (Return of the King!)
- I have no idea what's going on here!
- This fight looks absolutely crazy now.
Pharos Sirius:
- Looks nice.
- Siren. Also huge close up cleavage.
- Watch out for floor crawling zombie things.
Haukke Manor (Hard):
- New lighting makes the place look pretty awesome.
- Original 1.0 dungeon music.
- Completely different instance, different route/layout, different mobs and bosses.
Treasure Hunt:
- Reminds me of FF9 choco hot & cold (minus the chocobo), you get a small piece of a map of a random location and have to figure out where exactly it is.
- It would have been cool if they actually did it like FF9. Make you do it on a chocobo, and instead of a map give you an oddly angled screenshot to find.
Duty Roulette:
- The rewards will determine if this is good or not.
- Reward includes Tomestones.
- Looks like you get a bonus reward (e.g. +10%) for queuing as a Tank, perhaps as a Healer too.
- Apparently there are 4 "courses" (low level, high level, story dungeons, etc) and you can do each one once per day.
- Duty text sounds like the higher level you are above the dungeon the bigger your reward is.
- The duty text also makes it sound like your reward is higher for beating it, meaning you get rewarded even if your story noobs suck and you don't win? Makes sense if you can only do it once per day.
PvP:
- Hard to discern anything from the clip. We saw this in beta anyway.
- I wonder if the vanity system will be allowed in PvP. I believe many games disable vanity for PvP so you can't hide what your real gear is. But that clip of the one team all in white armor made me think it'd be pretty fun to have a PvP team that used the vanity system to dress up for fights. Always in bikinis, always in reindeer suits, always wear chocobo masks, always in pink, etc. Could become pretty notorious among the PvP scene this way. Be the equivalent of always turning up for your PvP fights like this:

Housing:
- Nothing we haven't seen.
- Still think Limsa's looks best.
Expanded story stuff:
- I didn't expect them to bother continuing the storyline until an expansion pack came along, neat.
- As long as you take out the majority of the damn quest filler, the 1-50 story missions were pretty good.
- Since these missions would all be level 50 now, I assume they won't bother with exp-quest filler; nobody needs exp.
Other:
- Hildibrand! I imagine anybody watching this trailer who didn't play 1.0 is confused as hell at this.
- Aesthetician looks kinda fruity.
- "Beast Tribe Quests" look kinda eh, although they do have a few new things like riding mobs.