What are some common mistakes students make with saturated solutions?
The 1 fatal error is to state that " a saturated solution holds a maximum amount of solute ". This is would be gleefully/regretfully (?) pounced upon by any examiner and marked wrong.
Saturation describes an equilibrium condition, namely "that the solution holds the same amount of solute that would be in equilibrium with undissolved solute" . As with any equilibrium, a temperature is usually specified, because a hot solution can normally hold more than solute than can a cold one.
Supersaturated solutions hold a greater amount of solute than would be in equilibrium with undissolved solute. You have probably seen some spectacular demonstrations of supersaturation after such a solution has had a seed crystal deposited, and masses of solute deposit (of course, after such an event the solution is once again saturated inasmuch as the solution has returned to equilibrium).
Why am I stressing this? Because questions regarding saturation are routinely poorly done at A levels, whereas a little care with definitions would give easy marks.