This is a little tough to figure out what's going on, but I'll give a stab at it.
I assume you're on the full auto mode, right? That means you've got your dial set to the "green box", not "P", "Tv", "Av", "M", or any of the other settings with pictures on them.
Is your "shutter faster" when you're taking pictures in bright daylight? And is your "shutter slower" when you're taking pictures in low-light situations, such as indoors? If so, then that's how exposure generally works. When there's a lot of light outside, the camera doesn't need to open up as long to get a good picture (in photography terms: the camera uses a faster shutter speed to get a good exposure). A faster shutter speed might be 1/500 second, for example.
When there's not a lot of light, such as indoors or night time, then the camera has to open up a lot longer to let more light in, so that it takes a good picture (ie. the camera uses a slower shutter speed to get a good exposure). A slower shutter speed might be 1/6 second for indoors or 1 second for night time, for example. With shutter speeds this slow, however, you're most likely going to get blurry pictures no matter how steady you're holding the camera.
However, you mentioned that there's a flash involved and that you're not getting blurry pictures. Is it "faster" when you're in a relatively brighter situation, where the flash goes off right away and the camera takes the picture right away? And when it's "slower", are you in a very dark setting, where the flash gives off an annoying, seizure-inducing burst of flashes before the camera actually takes the picture?
If that's the case, then it's what VVFF mentioned above. If your subject is in a dark area, the camera uses the flash to make your subject bright enough to help the camera get a focus lock on your subject. If you're in a very very dark area, then the flash might have to burst several times before the camera gets a good "look" and gets a good focus lock on your subject.
In terms of solution, the cheapest thing to do would be to take pictures in brighter situations. For example, if you're indoors, turn the lights on in your room before taking your picture, so that you don't get that annoying burst of flashes. See if that helps.
The only other thing I can think of would be to buy an external flash, such as the Canon 430 EX II for $300 or the Canon 580 EX II for about $400. Both of these flashes use a red focus-assist light that looks like a laser shining on your subject, allowing your camera to get a focus lock without that annoying burst of flash. However, I kind of hesitate giving out this recommendation cuz it seems like throwing more money at the problem without understanding the basics of photography.
The other thing you can (and should) do is invest in a good Intro to Digital Photography book. Your local bookstore (and library) will have TONS of these books. One that's highly recommended on this message board is "Understanding Exposure" by Bryan Peterson [
link to
Amazon]. Learn the basics of photography (such as exposure, shutter speed, aperture, ISO, etc), so that you'll know what your camera in "Auto" mode is trying to do.
Oftentimes, the camera in "Auto" mode doesn't know what you're trying to take a picture of, so it makes a best guess. It does pretty well in bright situations. "Auto" doesn't do so well in lower light situations.
Sorry for the rambling post. I wasn't sure of the details of your camera situation, so I, too, made my best guess.

Hope that helps a little.