"The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States."
I would suggest that "if" Sheriff Joe has taken an oath to support the Constitution that yes, he has standing. If he has taken such an oath as part of his official duties, he cannot be denied the opportunity to ensure that his oath is being carried out in full. He has a legal right to know whether any portion of the document he swore to uphold is being trampled or not enforced.
In order to bring suit a plaintiff must be able to demonstrate DIRECT and particularized injury from the action of the plaintiff. Think of a two car auto accident, a bystander who saw the accident but was not injured in it does not have standing to bring suit.
There are four people in the United States who have standing to sue Barack Obama for injuring them directly by denying them the presidency. Those people are John Mc Cain, Sarah Palin, Mitt Romney and Paul Ryan, the only people to receive actual Electoral votes and have a legitimate chance to be president if Obama is ineligible. They were DIRECTLY harmed. None of those four chose to file suit.
Average citizens had standing to file ballot challenge lawsuits against Obama to try to keep him off their state’s ballot. There were 50 such lawsuits in 2012 and they were heard in 22 states. No ballot challenge has yet prevailed however. Many of the ballot challenge lawsuits were filed by average Americans who don’t believe that Obama is eligible; people like Sharon Meroni in Illinois or Tracy Fair in Maryland or Al Hendershot in Alabama, et cetera.
Sheriff Joe could be a co-plaintiff, as could every other American citizen.
However there are no issues of standing if a law enforcement officer like Sheriff Arpaio pursued CRIMINAL charges against Obama for forgery, fraud, election fraud, document tampering, or other criminal activity.
Standing is not an issue in the criminal courts.
No law enforcement officer has presented a criminal complaint to a prosecuting attorney such as a district attorney, a US Attorney or a state attorney general.