I dose magnesium to go with the Randy diy 2-part.
The magnesium needs to be in balance with the calcium for building stony skeletons. (on lps, I've seen tissue recession on blastos and others if the magnesium gets too low).
I'll have to admit I originally started dosing iodine in a voodoo sort of way. I'd asked about it at a couple LFS. One has amazing zoas and mushrooms, the other has a long established display tank of crazy intense sps. Both stores dosed iodine "for better color", and neither tested for iodine levels.
At one of the stores where I asked about iodine, the owner said he used it in all his tanks. I must have looked kinda skeptical, because he walked me around to the side of his display tank, and pointed to all the big empty jugs of iodine supplement laying on the floor. (I guess he could have been faking, but even I'm not that cynical

)
I asked if he tested for iodine, and he said, "No. Test kit too expensive." I asked how much he dosed, and it was 2x what the directions on the bottle said to use.
So, based on how good their corals looked, I figured they must know what they're doing. So I started using iodine also. I used the daily dosing method rather than the weekly, and I dosed at 1x the rate given in the directions, and later went to 2x.
After a while, I picked up a Salifert iodine test kit, and found out that for my tank, dosing at 2x the rate put my iodine right within the recommended range. Since then, I've just kept up the dosing. I've been too paranoid to try controlled experiments with and without iodine to verify any benefits though.
Some things I've noticed... on the softie tank, if I neglect to dose iodine for a while, and then I add some, the shrimps will molt the next day.
People will tell you that if your xenia is not doing well, it's because it needs iodine. I've found that alk is more critical for xenia than iodine, and I've still had xenia do well when iodine was low.
As for iodine and mushrooms, I had some yumas and rhodactis get faded looking a long time ago. I started using iodine for them, and didn't really find a big difference. Later, I found that even at the bottom of the tank, they were getting too much light from MH. After I moved them to a softie tank with Home Depot shop lights, daylight and actinic tubes, the colors came back.
As for strontium or other trace elements, I rely on water changes for those, and don't test for them.