How dangerous and expensive was the construction of the "Cactus Dome" on Runit Island? There was news that the dome is leaking radiation into the groundwater and the Pacific, and I couldn't find much information on how the dome was created or what troops built it. How did weapons testing cleanup in the Pacific compare to meltdown cleanup in Chernobyl?
There is a somewhat recent survey report from Lawrence Livermore National Laboratory (LLNL) A Visual Description of the Concrete Exterior of the Cactus Crater Containment Structure from 2013 which describes the construction of the structure and its state in 2013.
In short, the waste stored under the dome is not highly radioactive. Most of the material under the dome is contaminated soil (mostly by Cs-137, a beta and gamma emitter) and Plutonium debris (an alpha emitter) that would be low-level nuclear waste if under US regulation. While none of this is material you want to live with, it is not promptly dangerous in the way spent fuel from an operating reactor is. The main hazard of both Cs-137 and the Plutonium debris would be by ingestion, rather than radiation as in Chernobyl.
It's useful to keep in mind that the cleanup took place 20 years after the last test on the islands, so many of the short-lived decay products would have decayed in the intervening years. In the case of Chernobyl, the cleanup operation was immediate, involving both contaminated debris and fuel assemblies from a mid-cycle reactor.
Also note that the total material stored in the dome is a very small percentage of the total contaminated material in the lagoon - the cleanup operation was to bring down the soil contamination of islands in the atoll by removing the most contaminated topsoil, not to collect all radioactive debris.