Hillary Clinton and Donald Trump traded snide jokes about each other Thursday at the Alfred E. Smith Dinner in New York, but it was Mr. Trump who set the high-society crowd on edge with sharp jests about his opponent’s “corruption.”

“Hillary is so corrupt,” Mr. Trump said about half way into his routine. “She got kicked off the Watergate Commission. How corrupt do you have to be to get kicked off the Watergate Commission? Pretty corrupt.”

The jab at Mrs. Clinton, the Democratic presidential nominee who was seated a few feet away on the dais, sent a hush over the crowd of dignitaries, politicians and media personalities at the quadrennial fundraiser for Catholic Charities.

The dinner has become an election year tradition, where the candidates typically deliver lighthearted remarks and poke fun at one another. This year, the dinner fell on the night following the final presidential debate.

Mr. Trump mentioned the WikiLeaks dump of Clinton campaign chair John Podesta. He told the crowd that they know Mrs. Clinton has “one public policy and a totally different policy in private.”

The crack provoked boos and jeers from the audience in the ballroom of the Waldorf Astoria.

“That’s OK,” said Mr. Trump. “I don’t know who they’re angry at, Hillary, you or I.”

“Here she is tonight, in public, pretending not to hate Catholics,” Mr. Trump continued amid groans from the audience.

“Hillary not laughing as much as the rest of us,” he said. “That’s because she knows the jokes. All of the jokes were given to her in advance of the dinner by Donna Brazile.”

More jeers.

Mrs. Clinton, who followed Mr. Trump at the lectern, also took some cheap shots at her rival, but the Manhattan crowd didn’t turn on her.

“Donald, after listening your speech, I’ll also enjoy listening to Mike Pence deny you ever gave it,” said Mrs. Clinton.

She made several jests about Mr. Trump’s affinity for Russian President Vladimir Putin, who she has claimed is trying to get the Republican nominee elected.

Noting that there wasn’t a teleprompter on the dais, Mrs. Clinton said that it was well known that Mr. Trump doesn’t like teleprompters.

“They are hard to keep up with, and I know it’s even harder when you are translating from the original Russian,” said said.

Later, she remarked on questions about her health, and Mr. Trump‘s.

“Donald really is as healthy as a horse, the one Vladimir Putin rides around on,” Mrs. Clinton said.

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