The asterisk is just 2.2's default way of labeling your gear sets. Prior to 2.2 it would just label it according to the ilvl of the gear set's weapon, but now it refers to the average ilvl of the set.

Before 2.1 or so, saved gear sets couldn't differentiate between identical armor that had different materia - e.g. you had 3 raptorskin rings, 2 socketed for miner/fisher, but the fisher one uses different materia. The gear set would just pick the two rings that appeared nearest to the beginning of the list rather than the correct materia. Now it picks the gear with the right materia, but you'll get that error every time you make any tiny change to the set without saving.