The main flaws that I am aware of boil down to the system not being as powerful as a PSP--don't expect the 3D graphics to be dazzling. Some games also use the touchscreen in odd ways, but obviously that's going to vary from game to game. The built-in speakers aren't that great, in my opinion. Fortunately, the DS Lite comes with a standard 3.5mm jack!
Battery life is good. I can get several hours out of a charge.
If you like RPGs, strategy games, adventure games, and platformers, then the DS is a good buy. If you like the GBA library, it's a good buy. If you prefer FPS games, action games, etc. you would be better off with a PSP.
The DS definitely has a greater focus on casual, accessible games. That said, you have some games like
Final Fantasy Tactics A2 which are ridiculously long, involved, and complex. Just the way I like it.
A lot of games, you can play without the touchscreen at all, or use it only as an occasional supplement. It's a nice concept, but I admit most games do not benefit from it at all, and some don't even use it.