This is what im getting constantly.
Especially when i receive my fates reward.
One thing i have noticed is, if you tab out for a couple of minutes the game starts lagging bad.
Your skill animations wont show but your damage will. If you click on your character profile it takes ages to come up. Then when playing for a few more minutes it will crash and give you the bottom error.

Problem signature:
Problem Event Name: APPCRASH
Application Name: ffxiv.exe
Application Version: 1.0.0.0
Application Timestamp: 529464f3
Fault Module Name: ffxiv.exe
Fault Module Version: 1.0.0.0
Fault Module Timestamp: 529464f3
Exception Code: c0000005
Exception Offset: 000ed42c
OS Version: 6.1.7601.2.1.0.256.1
Locale ID: 1033
Additional Information 1: 0a9e
Additional Information 2: 0a9e372d3b4ad19135b953a78882e789
Additional Information 3: 0a9e
Additional Information 4: 0a9e372d3b4ad19135b953a78882e789

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I run
Intel Core2Duo 3.0Ghz
4G Ram
ATI Radeon HD5770

Game runs smooth on medium settings but still crashes.
I really hope SE takes a look into this issue