That sounds like a graphics issue. I'm no expert but if you haven't already tried it, do the usual: Update your graphics card / DirectX drivers. If that does not help I'd try running the benchmark (http://na.finalfantasyxiv.com/benchmark/) just to see if that also wigs out. At least you'll know if its a general graphics problem with the game or something specific to the game client itself.

Sometimes it can be the smallest of things: Like having a program running in the background that conflicts with FFXIV. Try terminating anything and everything you could possibly think might have an issue with the game. (Like Fraps or Voicechat overlays - I'm looking at you TS!)

If the problem persist theres only one way: Contact SEs customer support.

I hope you get it sorted out and you'll get to play with the rest of us!