Sometimes I get these weird white reflections, that don't look real at all. I have a white sunlamp in the scene. Is there something I can do to stop this?
10x smaller sunlamp, added glare (perfect ad for a washing up liquid).
That is the reflection of the sun lamp. The size is related to the size property of the lamp. If you change it to 0, it will disappear. You will also have perfectly crisp shadows.
The sun lamp reflection looks unnatural because cycles produces a perfect reflection, instead of the soft edged sun were used to seeing because of the atmosphere. And there is no bloom that happens in your eyes or in cameras to bright objects. More info
So instead, You can add the bloom as a post process.
Or, use HDR an illumination map instead of a sun lamp.
Or, on the lamp, uncheck the box for "Multiple Importance". If the glossy shaders have no roughness, or set to "Sharp", the glint with disappear...