Washington Post fact checker Glenn Kessler gives a maximum of Four Pinocchios to the claim that Hillary Clinton was fired during the Watergate inquiry, which has gotten a lot of circulation on social media. He makes a detailed case that there is no evidence for such a firing. However, along the way, he does note some unflattering aspects of her tenure there:
In neither of his books does Zeifman say he fired Clinton.

But in 2008, a reporter named Dan Calabrese wrote an article that claimed that “when the investigation was over, Zeifman fired Hillary from the committee staff and refused to give her a letter of recommendation.”
The article quoted Zeifman as saying: “She was a liar. She was an unethical, dishonest lawyer.
She conspired to violate the Constitution, the rules of the House, the rules of the committee, and the rules of confidentiality.”…

In 1999, nine years before the Calabrese interview, Zeifman told the Scripps‐​Howard news agency:
“If I had the power to fire her, I would have fired her.”
In a 2008 interview on “The Neal Boortz Show,” Zeifman was asked directly whether he fired her.
His answer: “Well, let me put it this way.
I terminated her, along with some other staff members who were — we no longer needed, and advised her that I would not — could not recommend her for any further positions.”

So it’s pretty clear that Jerry Zeifman, chief counsel of the House Judiciary Committee during the Watergate inquiry, had a low opinion of the young Yale Law graduate Hillary Rodham.
But because she reported to the chief counsel of the impeachment inquiry, who was hired separately by the committee and did not report to Zeifman, Zeifman had no authority over her.
He simply didn’t hire her for the permanent committee staff after the impeachment inquiry ended.

Kessler also notes that Clinton failed the D.C. bar exam in that period. She never retook the exam (passing the Arkansas exam instead) and concealed her failure even from her closest friends until her autobiography in 2003.
And then there’s this:
Zeifman’s specific beef with Clinton is rather obscure.
It mostly concerns his dislike of a brief that she wrote under Doar’s direction to advance a position advocated by Rodino — which would have denied Nixon the right to counsel as the committee investigated whether to recommend impeachment.
That brief may get some attention during the next few years, should any members of the Clinton administration become the subject of an impeachment inquiry.
Also in Sunday’s Post, George Will cites James Madison’s view that the power to impeach is “indispensable” to control executive abuse of power.
https://www.cato.org/blog/was-hillary-clinton-fired-nixon-impeachment-inquiry