Lens technology has come a long way since the days of simple point and shoot cameras of a few years ago. It is now possible to correct many lens faults and color shifts because qualities of optical glass have improved considerably over the years.
It is a fact though that many compact digital cameras still suffer from barrel and pincushion distortion. Some cameras suffer more than others and in fixed focal length lenses the effect is less prominent than in zoom lenses. This form of distortion is brought about by the way modern zoom lenses are constructed and is dependent on the focal length used. Usually zoom lenses at their maximum wide-angle setting will suffer from barrel distortion which will gradually shift to pincushion distortion if you zoom to tele.
Closing the aperture will not lessen the distortion as it does with other lens faults such as lack of contrast or light loss in the corners of an image which usually only become apparent at maximum aperture.
In general photography distortion may hardly be noticeable, but when capturing buildings, horizons or other subjects with straight lines, barrel or pincushion distortion may be clearly visible. There are possibilities to correct them in your image manipulating program.