Instructions
Acquire an original PlayStation memory card for your games; PlayStation games cannot save to PlayStation 2 cards, and vice versa. However, you can copy PlayStation save files to PlayStation 2 memory card as a way to back up unused files and save space on your PlayStation memory card.
Make sure that you're using the correct functions on your controllers; if you choose to use a DualShock 2 controller, which uses analog buttons where the PlayStation controllers did not, ensure that you're pressing the buttons hard enough that the game registers them.
Use the right MultiTap -- the hardware that allows you to connect up to four controllers to your PlayStation system -- for the right system; PlayStation games will not recognize the the PlayStation 2 MultiTap and vice versa.
Avoid using hardware like the GameShark or Action Replay for the PlayStation on the PlayStation 2; because these interact with the PlayStation hardware directly, it can have trouble interacting with the PlayStation 2.
Turn off texture-smoothing and fast-loading; you can do this by pressing the "Triangle" button on your controller while the PlayStation 2 is on the browser menu. Select "PlayStation Driver" and press "Triangle" again to change your settings. These settings will need to be change each time you restart your PlayStation 2 and will not guarantee function for all PlayStation games.