My Logitech F310 was working flawlessly since 'forever'. I tried another controller & the F310 was glitchy. Here is the fix I worked out for my setup -
I had heard that people had a conflict with the Nostromo keypad Which they fixed by essentially unplugging/uninstalling the device while playing. I have a Logitech G13 keypad connected to my rig so I looked at the configuration. I had a driver for 'G13 joystick' installed so I tried disabling that (in device manager). Problem went away!
If you have tried different controllers, you also need to check the POL setup. To do this, go to "C:\Program Files (x86)\PlayOnline\SquareEnix\PlayOnlineViewer\polcfg" and run 'polcfg.exe'. Be sure 'use gamepad' is checked and that when you click on the Gamepad Configuration button the controller you want to use is selected in the drop-down box.

Hope this helps.