An NPR article published July 12, 2019 notes that, in addition to the Department of Labor:
Many other key agencies are also led by acting officials, including the Federal Aviation Administration, the Food and Drug Administration — even the president's chief of staff Mick Mulvaney is in an acting role.
The article goes on to note that:
The number of acting officials also means a dminished role for Congress, because various departments and agencies are being led by officials who were not confirmed for their jobs by the Senate.
Most recently, Trump has announced that Rep. John Ratcliffe is his pick to be the new Director of National Intelligence, which has prompted some to question whether
Ratcliffe [would] be so much of a loyalist that he would tell Trump only what he wanted to hear — and Congress and the public what Trump wanted them to hear
If Trump never formally nominates Ratcliffe to his position, what recourse might Congress have if they don't approve of him? Can someone in an acting role be impeached, for example? Would it be possible for Congress to interpret Trump's tweet announcing Ratcliffe's nomination as necessitating a formal confirmation?
I am pleased to announce that highly respected Congressman John Ratcliffe of Texas will be nominated by me to be the Director of National Intelligence. A former U.S. Attorney, John will lead and inspire greatness for the Country he loves. Dan Coats, the current Director, will be leaving office on August 15th. I would like to thank Dan for his great service to our Country. The Acting Director will be named shortly.
As noted by BobE, the Federal Vacancies Reform Act of 1998 will likely play a role here, as it dictates (1) who can be an acting official; and (2) how long an acting official can serve. So the question might need to be more narrowly defined: During the normal term of an acting official, what steps can Congress take? I would think impeachment is also an option. However, it seems that Congress may also be able to introduce new legislation to deal with the issue.