When we first got our point and shoot dig camera (fuji finepix) I was used to shooting film on an A1. We used to get blurry photos all the time.

On our camera we noticed that even after the camera shutter noise the camera wasn't actually done taking the picture. So what was happening was we would move the camera after the noise and it was still trying to capture the scene,

Hold the camera real still, tuck you elbows into your waist, slowly press the shutter, and wait a second after you here the noise.

We still get blurry pictures in low light without a tripod due to either the subject moving or we move ourselves. Movement on either end while the shutter is open will result in soft to blurry images.

Hope this helps,

Tim