As seen in the examples the pictures shot at higher ISO are more likely to present this problem. Also the combination between resolution of the camera and image sensor size plays a fundamental role in the process.
Chromatic aberration on the other side is generated by the lens and also depends on the focal length and the focus. "Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image, because each color in the optical spectrum cannot be focused at a single common point. Since the focal length f of a lens is dependent on the refractive index n, different wavelengths of light will be focused on different positions."
In this case the phaenomen is seen in the corner of the picture or between a tight pattern. Usually more expensive lens have built-in system to eliminate the aberration and to get the sharpest picture possible.
In conclusion I think that this two "errors" that the camera and lens produce can really affect the quality of the pictures but it's also fairly easy to compensate their effect to make the picture look good. Keeping the ISO level as low as possible and shoot with a good lighting should avoid the image noise presence in the picture. A cheap way to eliminate chromatic aberration from our pictures is to use a post production software that could automatically spot the defective areas and can erase the coloured fringes. Obviously higher the price of our equipment the lower we would notice this problems but even using cheap equipment is possible to take stunning pictures.