Connectivity
On some wireless controllers, the connectivity between the controller and the receiver could present issues. The receiver has to connect to the console and receive the signals that the wireless controller sends. Problems can arise if something else interrupts that signal, like a competing signal from a microwave, Wi-Fi router or another controller (or anything broadcasting on the same radio frequency). A piece of metal between the two devices can also cause issues.
Latency
Latency, or lag, is a simple but potentially detrimental problem. When a signal is sent out from the controller, it has to first be picked up by the receiver, then translated and sent into the game. All of this happens in a split second, but that split second is more than it takes to transmit the signal from a wired connection. This can be a problem because, in a game that's about split seconds, you could be just a hair too late. This is a problem with most, if not all, wireless PS2 controllers.
Receiver Fuse
The PlayStation 2 has a specific fuse that's used to power the rumble feature on the standard controllers. Some brands of wireless PS2 controllers use this fuse to power the receiver. If the fuse burns out, the receiver can't get power and can't read the signal coming from the controller. This is a huge issue because it effectively wipes out the controller.
Durability
One of the issues that's traditionally associated with third-party controllers is that of durability. Controllers made by Sony are designed to work perfectly with the console. A third-party controller is one made by any other company, such as Pelican or Mad Catz. They're made to compete with the more expensive Sony controller, and they can be made of cheaper material. Third-party controllers have a reputation for being lower-quality and less durable.
Battery Life
A wireless controller has to power itself. When the controller is connected directly to a console, it draws its electricity from the console. When it's wireless, it's going to need a way not only to broadcast the signal, but if you're using the rumble feature, it has to also receive that signal. Turning off the rumble feature does save battery life, but some controllers will last longer than others. It also helps to remember to turn the controller off after play, because even with an auto-off feature, it will run unnecessarily until the auto-off kicks in.