Also, be wary. My Sim is a Global Superstar and he got a notice recently that his star was dimming and he would lose one, if he didn't so something about it! So, while you don't gain more points, you most certainly can lose them if you don't constantly maintain your Sims' status. IE do those interactions with the Fame + next to them, mingle with fans, sign autographs, do Selfies, update your Simstagram and check on the online stuff. I have worked my newlywed, new Dad star's hind quarters off just yesterday in my game, trying to prevent any slippage. Balancing private life and public life can be a hassle, but he's also fond of eating, too.
Also, I believe the quirks that come along are random. Some may be interaction based, not sure about the rest. As @dizzydee_k said, there's always the celebrity cleanse.
