Dredging can unearth all kinds of various rock, soil, and shell materials and it's what they call dredge spoils. These dredge spoils set unconformably on uninterrupted soil and have the potential to form anthropogenic landforms such as lynchets and undulations. Unfortunately, the main dumping spot for dredging spoils is in the middle of the ocean and it can cause a bevy of issues.
Dredge spoils can be dumped elsewhere, such as on land for things like local land reclamation but the vast majority ends up in our oceans. This was initially started because it was thought that the ocean was vast enough to be able to hand the mixture and disbursement of soil and mineral waste. The size of the ocean kept those at ease for anything possibly going wrong, but it is now being paid more attention to as it has caused issues with fishers and disrupted the ecosystem.
This has prompted environmental organizations to regulate where these dredge soils are dumped. These types of regulations started at an event called the London Convention back in 1972. It has since been updated in 2014 which utilizes the best environmental options for dumping dredge soils and allows it to be more manageable and not so damaging to parts of the ecosystem.
In the short of it, dredge soils don't cause a health threat or life-threatening issues to humanity, but they will affect the world around us even if it may be ever so slightly.