problems with night pics

i have had a lot of fun with this camera. it is easy to use but since it is my first digital i cannot compare it to any other. however, every time i use the night flash i get blurry pictures. if there is action going on such as dancing, i have to use the sport selection in order to not get blurred pics. but if it is fairly dark i don't get enough light using the sport selection and then the pictures are dark. even the lights that are not moving look as though they are flying through the air. my pictures also look like double exposure. i seems as though my shutter speed isn't fast enough for night even with the flash. not sure if this is a problem with me or the camera! but it is so much fun and so easy to use that i'm hoping i can take it to someone who can help me out with that.