I use a Memory Card for the PSX, and the controller always used to work perfectly fine.
I found the disc a few weeks ago (I had lost it) and the controller still worked excellent until I was about to enter the Mysidia Cave, then it started doing this crap all of a sudden.

Does my using the PS2 display settings Fast and Smooth have anything to do with this?
I think I started using those settings somewhere around Mysidia Cave.