The main benefits of static lighting should be fairly obvious:
Low resource usage, as all of the lighting is precalculated
It can look nicer, as there's no limit on how long the lighting algorithm can run on a single scene
Basically put, static lighting is a good choice for lights and objects that are static in a scene. As they won't shift their positions, there's no need to recalculate the effect of these lights on the same objects again if it doesn't change the resulting visual effect of the scene.
The same applies for shadows. Pregenerating them allows many more high-quality shadows than doing it in real time, especially when the target platform is quite limited in terms of resources, which is often the case on a mobile platform.
The disadvantages of static lighting and shadows should be fairly self-evident as well:
Static lighting, by definition, does not affect objects that move through a scene.
Static shadows are not affected by dynamic objects...