I just finished all the quests given to me by whatever her name is in the waistworks of Hlaalu canton in Vivec and she tells me to see Curio about more business, but when I go to see him, he won't give me any quests. Am I missing a step somewhere or is this a glitch?

You have to be at a particular rank before he accepts you as a protege. Check advancement. If you haven't done enough quests, Edryno Arethi in the Treasury in the Hlaalu compound will give you several and Ilmeni Dren in St Delyn has three (though you have to be a certain rank to get her quests too).