Only really works in places that are rich in key nutrients but aren't yielding much growth, iron is a very minor nutrient but sometimes that's the only thing missing. Anyway, the problems are mostly complete unknowns, like what kind of changes or how much of a change. There's also the problem (as some people have mentioned) where oxygen levels in the deep sea might drop due to excessive detritus.
The sequestered carbon is pretty much all calcium carbonate (basically chalk) from the dead plankton. I would say a better idea would be to stimulate calcifying plankton by adding calcium, which could be upwelled from depths above the Carbonate Compensation Depth (where the calcium carbonate dissolves faster than it accumulates). The problem here is whether or not this causes sequestered carbon to be released, as well as all those issues with the iron fertilization regarding messing up ecosystems.