Never a problem with the screen apart from a stuck pixel which was covered by warranty.
This, however, must be a first (at least to my knowledge):
About a month after I started playing Castlevania: Dawn of Sorrow, I would press the jump button (B) and occasionally the DS would simply turn off. This happened randomly, but I had no idea what it was due to.
I went to the repair center and they told me it was because the mainboard was fractured right around the B button, but it was under warranty, and they would replace it free of charge. I asked the guy if they ever encountered something similar, and he replied in the negative.
I guess I just have to watch the amount of force I use when pressing buttons on the DS!