Digital cameras are slow, period. They can take anywhere from five seconds to half a minute to store each picture once you've pushed the shutter button. So don't expect to take rapid-fire sports shots. On the other hand, five seconds is a lot better than half a minute if you're taking candid photos or have people waiting for you to shoot their pictures. If speed is important, choose a camera that processes photos quickly.
Digital cameras eat batteries alive.
This can get very expensive. Look for a camera with a rechargeable battery. Better yet, get one that can be recharged while it's in the camera. That way you can always carry spares. There are some weird-looking digital cameras out there.