I think they did a really poor job of making the game social. The worst part is when you do dungeons from the duty finder, once you're in there, everything else about the person seems to be stripped out - you can't see what guild they're in, what server they're on, and can't message them after the dungeon is over. There's no way you can keep in contact with people if you end up enjoying the experience as it's designed to be short term and disposable. Quests can be done by yourself, and will even not let you proceed in many of them if you have someone else with you. FATEs are entirely mindless requiring no skill or strategy up until maybe the last ones (I've only found one that requires some coordination)
I really enjoy the game a lot (when I can get in) but as far as criticisms for what went wrong, I think they went an opposite extreme from FF11. Instead of being forced to party up to complete your objectives, you can play almost every single piece without having to interact with anyone - and your interactions with others are brief and forgettable.
This game is, in fact, very anti-social. At most you'll see a lot of socializing within your free company, but those will be separate little bubbles. Linkshells are a smaller, although similar bubble-like, alternative, but I don't expect those to be around in force a few months after launch. This anti-social quality is common for MMORPGs, outside FFXI that is. Even WoW players recognized the effect of taking things off server (and into instances) does to a wider community.
Matchmaking in Call of Duty has stronger potential to make friends than Duty Finder - you can easily reconnect with anyone you play a match with and there is no difference from "server" and "off-server" expectations (Duty Finder is already infamous for its bad players, so some people will go into it pessimistic and apathetic).
Outside of Duty Finder, FATEs were designed to be as solo-friendly as possible, much to the determent of interesting content (outside the handful at endgame they decided to put some effort into designing) and creates a way to quickly level to 50 by just blindly spamming your AoE attack while alone among others.
One downgrade of Version 1.0 is that outside dungeons and primals, they made sure quests were strictly solo friendly - turning the Artifact Quests from a community-building pseudo-endgame (just like it was for FFXI, really) into joke filler content and AF into nothing more than gear made irrelevant by the time you are doing lv. 50 dungeons a few levels later. (Really weird how they can go so hard into two different directions. Something like Garuda exists in the game, yet AF is main scenario side-quest quality.)
In terms of battle system design (how FATEs can work the way they do), there is virtually no direct cooperation. Tanks do their tanking thing, healers keep bars up, and DDs keep damage up, all of them only concerned with their own persons when it comes to dodging marked red areas (vs. something like a "stun" order from FFXI). There is no replacement for skillchains, magic bursts, sneak attack+trick attack (having someone screw over your positional attack is less of a loss in this game as individual weapon skills are far less important), or non-linear enmity gain that requires players to be more in sync with each other. I also think the lack of meaningful relationships means people are more willing to be utter fools in public, but that could just be the game hasn't outworn its live beta-like feel yet.
Also worth noting is that FFXI (and 1.0 to a lesser extent) was a true international game where people around the globe interacted on a face to face basis every single day, influencing each other's sub-culture and etiquette (e.g. player lines for content showing up in a lawless MMO world). FFXIV: ARR, like most games, is not.
I think the community aspect is going to be complete crap. However, this is the norm of MMORPGs. Just like quest hubs with hundreds of filler quests, etc. So at worst, "this alone in a city" feeling will be accepted in apathy by FFXI players and most other MMORPG players will be oblivious to it.
If nothing else though, I really want to someone to bring up duty finder and FATEs (and AF quests) to Yoshi-P at the same time. He's spoken a lot about "community", but I don't think he understands it (he didn't play FFXI, so whatever). When people bring up Duty Finder's anti-social mechanics, he mentions FATEs as a way to connect. When people bring up FATEs solo-focused, anti-social mechanics (though what they really are is people hitting one button until everything is dead), he mentions dungeons - which are primarily done through duty finder.
EDIT: And what's interesting is that, whenever people say "this game isn't going to be F2P" they usually mention FFXI's success. Given everything I've said above, why are we applying FFXI's history to a WoW-clone game? There is nothing to say they will be received similarly, at least long after the launch of a "Final Fantasy" game. People played FFXI (and put up with a lot of shit) for a decade because of the bonds they formed (partially because of that "shit", depending on how averse you are to inconvenience).