All those images appear to have been taken with flash and the shadows ruining them all look as if something is partially obstructing the flash. It could be any number of things (looks the same in some images, different in others)... a strap, a lens hood or the lens itself (in the case of a large lens), or a finger or two.
See: http://www.expertphotography.com …ds/2012/01/1-standing.jpg
This shows bad and good techniques holding an SLR camera, that I think is what alunh is referring to.
Basically, grip the camera with your right hand, cradle the lens or lens/camera (depending upon how large the lens is) upon your left hand. Keep your elbows tucked in against your torso. Stand with your feet about shoulder width apart.
Shadows like that are often caused by folks holding the lens from above, rather than cradling it on their hand. Held incorrectly from above, people are unaware their fingers are partially obstructing the flash (and possibly sensors or other things on the front of the camera). The correct holding method is also shown on page 38 of the manual that came with the camera.
I thnk it pretty unlikely, but suppose it is possible that something is loose inside the flash head, moving around and obstructing the shots partially. In other words, it might be a fault with the gear, instead of "user error".
If you intend to shoot a lot of flash, you might want to consider getting an accessory flash to use, instead of relying upon the one built into the camera. The built-in flash on any camera is pretty weak, in the worst possible place for redeye and ugly shadow effects, and it rapidly draings the camera's battery. All these are solved by an accessory flash, many of which allow you to tilt the head and bounce light or add a diffuser for nicer effects. Direct accessory flash can be improved even more by putting it on a flash bracket and connecting it with an off-camera shoe cord. This moves the flash away from the lens axis, which further reduces the risk of redeye and tends to put shadows down and behind subjects, out of sight (when done right). Built-in flashes might be helpful in an emergency, but I wouldn't rely on them regularly... accessory flashes do a far better job.
Oh, and I also highly recommend you consider using both a camera strap and a lens hood... both do a lot to protect your camera and lens.