You probably haven't done anything wrong. Bodies will hold and release weight or water when they feel like it. Don't sweat it , keep on with the plan, you'll be fine.
Maybe you could try only weighing once a week, so you don't notice the ups and downs of your weight so much?
A lot of people say the artificial sweeteners in diet pop and chewing gum will slow down or stall your weight loss. The sweet taste definitely makes me have cravings. Maybe you could try going back to plain water for the rest of your induction.