[dan on the right]

What standing does a plaintiff in a lawsuit have to claim that the person who runs the defendant entity wasn’t properly appointed?

None.

[Alberta's Child]

See Post #16. In a case where the "defendant entity" is responsible for overseeing a legal process involving the plaintiff, the plaintiff probably has all the standing they need.

In the NLRB case I cited, the "defendant" in that case was functioning the same way as the plaintiff in the Maryland case -- by challenging the authority of the NLRB chief counsel to take disciplinary action against SW General, Inc. over alleged labor law violations.

SW General, Inc. won the case.

Interestingly, it was a 7-2 decision. Even Breyer and Kagan agreed that Obama was completely out of line in appointing the NLRB's chief counsel without Senate approval.