Point and shoot digital camera sensors are quite different from digital SLRs in that they are mounted to the back of the lens assembly and housed internally within the camera. Accessing these sensors can be quite tricky in regards to camera repair, as it requires removing the covers of the camera, and many circuits in some cases.
It is important to note that digital cameras with built in flashes have high voltage circuitry housed internally, and as any camera repair technician can tell you, it is not a pleasant experience to be shocked by these circuits. Contaminated images in digital point and shoot cameras can be caused by dust/debris on the filter or between it and the sensor itself. They can also be caused by debris in the lens assembly. This is only visible in images if it is on the autofocus lens group closest to the sensor assembly. Dust or debris behind the front lens group is less likely to be visible in images.
It can be quite complicated to disassemble the lens to reach the source of the contamination, and again the lens elements and filter are highly sensitive to scratching. Once the sensor has been cleaned, it is important to keep the camera clean, use a lens cap if provided, or store in the appropriate case when not in use. Try to avoid using the camera in conditions where it may become exposed to fine particulates as they can be drawn into the lens assembly during use.
If cameras are kept clean they will require sensor cleanings a lot less often. Annual cleanings are highly recommended, but if a camera is used heavily or exposed to the elements, it should be periodically inspected to determine if it is in need of professional cleaning.