While at BYU, Griffith took a two-year leave of absence to serve as an LDS Church missionary in South Africa.

In that position, he gave nonpartisan legal advice to both parties during President Bill Clinton's impeachment trial.

Controversy arose over Griffith's nomination because his District of Columbia bar membership had lapsed in 1998 for failure to pay dues.

After the Washington Post ran a story about the issue in June 2004,[5] a number of prominent Democrats wrote letters supporting Griffith.

[6] Seth Waxman, who had served as Solicitor General under Clinton, wrote that "for my own part I would stake most everything on [Griffith's] word alone.

"[7] David E. Kendall and Lanny Breuer, two of Clinton's lawyers during the impeachment trial, also wrote letters supporting Griffith.

Despite earlier criticisms of Griffith, the Washington Post endorsed his nomination, noting that he was "widely respected by people in both parties" as a "sober lawyer with an open mind".

[16] In April 2021, President Joe Biden named Griffith to the Presidential Commission on the Supreme Court of the United States.

[17] In September 2022, Griffith was one of two candidates proposed by the government as a special master to review documents seized in the FBI search of Mar-a-Lago.

[18] In July 2023, Judge Christopher R. Cooper of the United States District Court for the District of Columbia designated Griffith as the mediator of a dispute between the United States Court of Appeals for the Federal Circuit and Federal Circuit Judge Pauline Newman.

2007): Griffith joined Judge Laurence Silberman's majority opinion holding that the Second Amendment protects an individual's right to bear arms and that this right is not limited to members of the military or organized militias.

2010): In an opinion for an en banc court, Griffith affirmed the dismissal of a defamation suit against the United States by owners of a Sudanese pharmaceutical plant.

Griffith affirmed the dismissal on the ground that the owners' allegations presented a nonjusticiable political question, writing that "courts are not a forum for reconsidering the wisdom of discretionary decisions made by the political branches in the realm of foreign policy or national security."

2011): Griffith wrote a unanimous opinion holding that there is no constitutional right to engage in "silent expressive dancing" inside the Jefferson Memorial.

The opinion noted that the government has substantial authority to impose reasonable and viewpoint-neutral speech restrictions on a discrete portion of its own property in order to create a tranquil national memorial.

In this case, the court held that dancing inside the Jefferson Memorial was prohibited "because it stands out as a type of performance, creating its own center of attention and distracting from the atmosphere of solemn commemoration that the [National Park Service Regulations] are designed to preserve".