The concerns she tallied about Mr. Gibson included: “Taking quotes out of context,” “Getting basic facts wrong,” and “engaging in distortionary hype.”

One of Mr. Gibson’s competitors, Bob Schieffer of CBS News, who had tried to get the first interview with Ms. Palin and is still seeking her for “Face the Nation,” said the ABC anchor had struck the perfect balance.

“I thought he was very respectful, which I think he should have been, and treated her with dignity,” Mr. Schieffer said in an interview. “But he also really bored in. When he didn’t get an answer to one question, he went in from a different way. I think that is what reporters are supposed to do.”

What was not in dispute was that people were watching. An estimated 9.7 million viewers saw the first part of Mr. Gibson’s interview with Ms. Palin on “World News” Thursday night, nearly 25 percent more than watched Mr. Gibson’s program a week earlier and two million more than watched “NBC Nightly News with Brian Williams” as Mr. Gibson was interviewing Ms. Palin, according to Nielsen Media Research. Often the audiences are similar in size.

Bolstered by its broadcasting of the second installment, “Nightline” on ABC was seen by more viewers than both “Late Show with David Letterman” on CBS and “The Tonight Show with Jay Leno” on NBC. Another installment, in which Ms. Palin chastised Congress for excessive spending and spoke of her personal opposition to embyonic stem-cell research, was shown Friday on “World News,” with a one-hour episode of “20/20” based partly on the interviews scheduled for later in the evening.