Good question. Don't know what became of any (if any) executive decisions Moodie made while in office for the 5 or 6 weeks he usurped that office.
I believe this would be some seriously uncharted territory.
If a person is not eligible to hold the office from the get go, under what authority could they then have made any decisions?
The same could be asked of Chester Arthur.
If no one brings the case against them, and is heard, I would assume nothing would happen to their decisions.
Someone (some people) would have to make a formal challenge.
Of course, the first challenge would be for those "in power" to determine that he isn't a "natural Born Citizen" as required for the office. Then, what he has done becomes the next challenge.
A federal court ruled on the question regarding Obama’s status in 2009. The ruling was appealed to the U.S. Court of Appeals and then again at the Supreme Court of the United States and it was not reversed, so it stands.
Barnett, Keyes, et. al. v. Obama, et. al.
U.S. District Court Judge David O. Carter: “There may very well be a legitimate role for the judiciary to interpret whether the natural born citizen requirement has been satisfied in the case of a presidential candidate who has not already won the election and taken office. However, on the day that President Obama took the presidential oath and was sworn in, he became President of the United States. Any removal of him from the presidency must be accomplished through the Constitution’s mechanisms for the removal of a President, either through impeachment or the succession process set forth in the Twenty-Fifth Amendment. Plaintiffs attempt to subvert this grant of power to Congress by convincing the Court that it should disregard the constitutional procedures in place for the removal of a sitting president. The process for removal of a sitting president—removal for any reason—is within the province of Congress, not the courts.”—U.S. District Court for the Central District of California, October 29, 2009
http://ia600204.us.archive.org/1/items/gov.uscourts.cacd.435591/gov.uscourts.cacd.435591.89.0.pdf