I had at least 4 problems total from all my DS consoles. Although, I grouped 3 of them together, since it was on the same console.
Anyway, the 1st problem on any DS console was on my White DS Lite. The hinge broke off/got loose, and the DS Lite ended up all dangly if you held it.
The 2nd problem was on the same console. The screen on my DS Lite had a thick line of dead pixels (located on the right of the touch screen). The dead pixels prevented me from seeing part of my game (at least on the touch screen).
The 3rd and worst problem was on the same console, again. The touch screen got all rough, and finally, it broke. It's pretty hard to explain what happened when I touched the touch screen with my stylus, but I'll try. Wherever my stylus touched, the touch screen would think that I touched at least an inch away right, from where I originally touched. Hard to explain, but basically, broken touch screen.