The term is caustics, also known as "fireflies". In Blender, the usual solution is to clamp the maximum brightness of an individual sample to a certain value.
@RCD-Y: I understand the noisy shadows in the previous examples due to precision errors. But I am still confused why there are so many bright spots. Do they occur for similar reasons?
Is this because of how we pick sample direction randomly for each bounce? So randomly picking the direction of the blighted spot on the ball?
I think they mentioned that there's some floating point errors that aren't counted for that could cause some intersection errors, which can cause something like this.