Some said Mr Trump kissed them without permission on the lips or put his hand up their skirts.
Standing at the site where in 1863 Abraham Lincoln delivered his famous defence of rights and freedoms for all mankind, Mr Trump spent the first portion of his speech again denouncing the electoral system as "rigged" against the American people.
He cited a Pew Research Centre suggestion that 24 million voter registrations are either invalid or significantly inaccurate and that 1.8 million dead people are registered.
Mr Trump then went further than the study, inaccurately claiming that some of these deceased citizens are "are still voting".
Mr Trump's campaign has taken a nosedive in recent weeks, with Real Clear Politics now showing him six points behind Hillary Clinton in a national average and losing in major swing states.
Laying out policies for his first 100 days in the Oval Office was part of an effort to resurrect his ailing campaign.
Mr Trump promised to form a contract with the American people to "bring change in Washington".
"My ethics plan will end the corruption: we will drain the swamp in Washington and replace it with a new government of, by and for the people," he said.
He urged Americans "rise above the noise and the clutter" of a corrupt election and "dream big" once again.
Mr Trump's reforms of Washington included a constitutional amendment to impose term limits on all members of congress.
He also called to reinstate a law banning White House and congressional officials from becoming lobbyists for five years after leaving their jobs.
In a move that will be looked upon with fear by climate-change experts, Mr Trump promised to lift restrictions on energy production in the United States.
He called for a return to coal mining, and an increase in fracking.
He promised to cancel billions of dollars in climate-change payments to the UN and use them to fix American water systems and infrastructure.
Mr Trump also promised to repeal and replace Obamacare with a system of "health savings accounts".
he Republican nominee has become increasingly bitter as his poll numbers have fallen.
At a North Carolina rally on Friday, Mr Trump railed against "corrupt Hillary" but much his delivery was less energetic than usual.
The man who once promised his supporters who would "win so big" there wouldn't believe their eyes, now contemplated the personal cost of defeat.
"What a waste of time if we don't pull this off," Mr Trump said.
"You know, these guys have said: 'It doesn't matter if you win or lose. There's never been a movement like this in the history of this country.'
"I say, it matters to me if we win or lose. So I'll have over $100 million of my own money in this campaign."
