The red dots are overmelds. This item only has one meld slot that will be a 100% success rate when trying to put materia into it. Any other melds done will suffer a penalty to success rate and the penalty increases based on the materia tier (I-IV). The penalty also increases for each successive overmeld.
The size of the dot, by the way, shows you what tier of materia was used to fill the slot.
The word perception is in red, because, although the materia used usually grants a bigger perception bonus, the particular item has reached its cap and is only allowing +3 of that bonus to apply to the gear.
Hope this helps.