The trust-building starts tomorrow!

New CBS News chief Bari Weiss gave a town-hall address Tuesday in which she decried the public’s lack of trust in the facts fed to them by journalists.

Regrettably, the journalist did so while presenting a slide that included a glaring factual error.

Smirking spies tell Page Six that Weiss showed her colleagues a chart comparing the Tiffany Network’s ratings over the last 30 years, or so, with those of rivals NBC and ABC.

But the lines showing the performance of NBC and CBS got transposed, so the chart showed CBS locked in a noble — if entirely imaginary — decades-long battle for network news supremacy against ABC.

It may seem like a relatively small oversight to the casual observer, except that CBS is virtually synonymous in the news biz with “third place,” while NBC and ABC have made headlines for years as they traded the No. 1 spot.

CBS insiders assure Page Six that it was simply an error, and the network wasn’t trying to show itself in a better light than it deserves.

Snickered a network exec, “For a network that is touting the importance of accuracy and credibility, this was sloppy.”

Meanwhile, an eagle-eyed PR pro noticed that there was also an on-air typo on the network Tuesday night.

When it teased a segment on brain health, there appeared an image of a grandmotherly woman holding an infant with the words, “Still Ahead… Brian Boost.”

Seems like a few people at CBS haven’t been using their Brians.

Then again, there was also a major gaffe over at ABC News on the same night when newsman David Muir introduced not one, but two reports that led to dead air to open the broadcast. An ABC source told the Daily Mail the glitch was due to a computer issue, and another source told Page Six that the incidents sent the network’s control room “into chaos.”

One CBS insider even quipped they’d rather have the typo any day.