Italicized text.....SE has not tested these cards., here is the currently supported list:
http://www.playonline.com/ff11us/env...tml?pageID=win
If toggling the graphics stabilization option doesn't help, then you will likely need to take this up with
nVidia at their support site for a driver fix, unless one has already been posted. There have been several threads in the last few years about not only FFXI, but other DirectX 9 or older games on the newer cards (back as far as the 400 series). In some of them, nVidia was working towards a fix, but not sure how far they got with it. Try searching either on your 650M and FFXI, or FFXI and 600 Series and you may get some good hits.
Edit:
Also, if your laptop is running the Optimus setup (has both an Intel HD400 and an nVidia graphics chip)--need to make sure to set which one to use for FFXI. On some of those hybrid laptops, people found they had to use the Intel Graphics because nVidia drivers weren't working worth a flip for FFXI.