As Mike has said looking at the front of the lens from different angles under a good light will clearly show up any dust cloud or finger prints on the front element. These will only show up on prints if a light source happens to be at the right angle to cause the flare.
Assuming that the lens is clean I've had a quick look at your gallery for any clues to the problem. I would say all except the church shot suffer from flare to some degree. The only difference would seem to be that the church was taken with the light from behind you and the others are against the light. I suspect this camera just does not fair well with against the light shots and I very much doubt that a lens hood will do much to solve the problem.
If you bought this camera from a local camera shop I would be inclined go back to them to discuss the problem and maybe they will let you exchange it.
I note that you seem to prefer to take shots of buildings. It is worth talking to the camera shop about the best camera lens for this style of photography.
Zoom lens on compacts are notorious for barrel and pincushion distortion at either end of the range which will be noticed more on building shots than the typical family group shot. A simple test is to take shots of a door frame at different zoom settings and see how they fair.
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