Well, this is not really ZSNES related, but since there are some knowlegdeable people in here there's a chance someone might have a clue.
In fact the controller is working perfectly with zsnes 1.50 and applications like Pro evolution soccer, though it isn't in some other emulators like pSX or ePSXe.
In the pSX pad config the cursor runs through the buttons and all of them get set like this
Looks like a little jitter on one of the analog sticks. Check your driver, and calibrate. If that does not help, look for a dead zone option in the driver (if there might be one present). If youre using a sony branded controller, try turning off the analog and see if it clears up at all. Also, try another playstation/ps2 controller if you have one present.