Challenging the inspector for approving work on the project is likely something a third party such as a neighbor would do. While there may be the option of appealing to an appeals board my sense is that the most productive approach is to sue the building department
If the property owner believed that the work was not appropriate, I would expect the owner would modify the construction documents, if necessary, and have the work done correctly
This is such a horrible idea. Instead of having a productive conversation expressing concerns over what may have been missed items, your answer is to just sue the building department?
Mark, you really do just hate building departments or something. I really wish you would get off your high horse, stop railing against code officials, and start promoting code officials and design professionals working together. You have some really great ideas, and a tremendous amount of knowledge. That said, your message is often lost on deaf ears because of your chronic denouncing of code officials.
For the OP, Building Departments are pretty much indemnified unless it is an act of malfeasance. Good luck proving that. All the BO has to say is "Oops, didn't see that." Lawsuit dismissed. Dont waste your time and money suing the BO. Even if you do prove the malfeasance (a one-in-a-million shot), the AHJ still wouldn't be the one on the hook for the repairs. The AHJ didn't do the shoddy work, the contractor did. The contractor should fix it.
Now, if the work (the home) is not code compliant, working with the BO may be able to get the CO revoked. With the CO revoked, you now have a solid case of presenting damages for suit against the builder. The builder would then be on the hook (depending on your contract with him/her) for making the necessary repairs, as well as any damages incurred due to their sub-code standard work.
For the OP, and Mark - Remember that it is first and foremost the contractors responsibility to perform construction in accordance with the adopted codes. The BO and his/her delegates are not present to guarantee, warranty, or provide any other assurance that a structure is code compliant. The role of a BO is to perform quality assurance and to spot-check the work of the contract to catch as many issues as possible. Will they catch everything? No. The contractor was responsible to build it right in the first place. The contractor is responsible for performing quality control over their own work, and the work of their subs.