Is the charge of an ion evenly distributed? This question relates to:
 Gauss' law and ions?
Is the charge distribution in an ion spherically symmetric due to quantum mechanical effects or do we assume it when using Gauss's law, as in the linked question, to make the calculation easier? 
I think it is the former but I am not sure.
 A: It will help you understand the quantum mechanical picture  if you read up on atomic orbitals. These are the loci around the nucleus where the electrons have a probability to be found. You will see that the orbitals  have a shape, which depends on the angular momentum of the state. The electrons carry the charge and thus you can interpret the plots as probability of the charge being there. They are not uniformly spherically symmetric except l=0. l=1 has two lobes and is elongated, and higher spins more lobes .
Now in the case of an ion, where an electron is missing: When close to an ion, as another atom will be, the shape of the positive charge will be the complement of the hole left by the missing electron, and it will not be uniformly spherically symmetric either, there will be lobes.
To assume that the single excess positive charge of the singly charged ion is at the center and be able to apply Gauss' law you have to be far enough that the details of the orbital shapes can be ignored. For milimmeter and micron distances this certainly will be true. For nanometer and smaller it becomes problematic and will depend on the specific problem one wants to address.
