Time:
From as early as 10:39 AM EST and still ongoing.

Frequency:
Every time myself and many others try to connect to event or instancing conditions (including, but not limited to, Palace of the Dead, job quests, Stormblood story quests, Duty Finder and Roulettes).

World name:
Cactuar

Character name:
Xoria Tepes

Party or solo:
Party and solo both.

I would like to say that at some point, a bunch of us were able to progress in the main story quest, the first instanced one for Stormblood, after hours of spamming the NPC (and probably amplifying the issue). However, most of the time spent was seeing the error:

A system error occurred during event movement.

Other times, like Palace of the Dead, or Duty Finder, is simply met with a long loading screen and then an abrupt 90002 error.