Metacritic scores...

Final Fantasy XIV - 49/100
Final Fantasy XIV: A Realm Reborn - 79/100 (PS3), 83/100 (PC)

It's safe to say that yes, they turned it around. XIV started with a lot of EoFFers trying it out and an extreme few sticking around. XIV: A Realm Reborn started with a lot of EoFFers trying it out and even more joining since after discovering it was getting good reviews.

It's hard to pinpoint exactly what went wrong at the start of the first game, and some people might simply say "Everything". I would point to the extremely many bugs, the extremely slow UI, the awful market system (although I'm not sure the new one is perfect, it's definitely better) and a copy/paste landscape where you feel like you're walking through a very large hall of mirrors sometimes. The old game did have it's good sides, though, and I'd argue some things were better in the original (such as the crafting / gear system and arguably the battle system, if not the pace).

The old game at it's final patch (1.23) was actually really good, though. The change of producer/director helped FFXIV untold amounts, and once Yoshi-P's work started being progressed through to patches, it really started to shine.