The number of pictures on the card does not affect the quality of photos. If you have an older digcam then you probably do not have image stabilization as a feature on your camera; in that case, you must use your flash to avoid shakey, blurry photos- or have a tri-pod- it's a bummer, and the flash can ruin the moment, but in order to avoid blurry pics, you've got to.
bad thing about flash, is the range in which the flash can reach- if you are shooting in a low light situation and use your flash but your subject is far away, the pic will turn out very dark even with the flash- it might be salvaged with editing... maybe.
If you are always in this situation of fast moving subjects or low lighting then you might consider getting a newer camera that has Image Stabilization and a super zoom. It can't hurt to wait until prices drop on those cameras since those features are newer and therefore kinda pricey.