Even if the wood is used in a home’s construction, the moisture in it will still continue its evaporation process. As the wood dries out it will shrink, and this can form gaps. You might see evidence of this with drywall and nails where a gap might form, forcing the nail to push through the drywall. While this wont necessarily cause major issues, it might not look very good.
Mold is another problem that can result from green lumber. The mold could even form on the wood during transportation which means the building might have a mold problem even before its completed.
Its not just water that evaporates from the wood but other fluids such as tree sap will continue to escape from it. This can cause staining and if the wood has been painted before the evaporation process has finished, it could start to bubble and look unattractive.
Green lumber is used because it is a cheaper option than kiln dried lumber. It will also dry out much quicker in drier, more arid States.