It's pretty indicative of all the point and shoots out right now. The problems your having are the reason why some move to the DSLRs, but then find the learning curve a little daunting.
After a year of using my Canon PowerShot A570 IS I am ready to get rid of it due to poor indoor shooting performance (flash recycling time). Having two youngsters, I often miss shots (even with fresh batteries) due to the flash. Not sure if this is problematic of all point-and-shoots are just this camera. My old Sony P52 was a better performing camera, though the pictures were not as sharp as the Canon.
Anyways, would like a recommendation for a new camera. Was looking at the Panasonic Lumix DMC-TZ5. Reviews of this camera or any other cameras in this general range would be greatly appreciate. The camera is primary used for taking pictures of my kids and for vacation pictures.