I dosed iodine regularly for the first 6 months we had our reef tank. Our shrimp and crabs molted regularly like clock work and there was excellent growth on many of our soft corals (especially Xenia and our Sacrophyton leather). I decided to stop dosing iodine for 6 months to see if there's a noticable difference. So far, there's no noticable effect on the growth or coloration of our corals, however, the coloration of our 4 shrimp is not as good as it was previously (could be some other factor besides iodine) and our shrimp / crabs don't appear to molt quite as often (although it is hard to tell for sure in a reef tank containing plenty of LR). I'm still performing water changes on the same schedule with the same salt mix (Reef Crystals). I'm not certain how iodine effects coloration of aquatic critters, but the intensity of the pink on a flamingo is suppose to be heavily related to the iodine content of their diet (i.e. how much iodine-rich shrimp they consume). Based on that, I can see that it's possible for appropriate iodine concentrations to be important for overall reef coloration, but certainly have no scientific evidence to point to as to what that concentration should be.
Otherwise, I dose calcium and alkalinity buffer as needed. I don't always test before making those additions, as regular testing for several months gave me good estimates of the rates at which both of those levels are depleted in our tank.
The only other addition that is not strictly food is Selcon, which I soak frozen foods in before feeding them to our tank.