Those are lens flares - Flare is particularly caused by a very bright light sources either in the image – which produces visible artifacts – or shining into the lens but not in the image – which produces a haze.
Most commonly, this occurs when shooting into the sun (when the sun is in frame or the lens is pointed in the direction of the sun), and is reduced by using a lens hood or other shade.
I've never run into hexagonal dirt or smudges.

An example of lens flare like yours:
