The forum, moderated by NBC News' Kristen Welker, featured several contentious exchanges.
One moment that caught Baier's attention was when President Trump brought up the ongoing controversy surrounding Biden's son Hunter's foreign business dealings, and allegations that the elder Biden either was privy to or profited from those ventures.
Baier said he expected the topic to come up at some point -- either at Trump's insistence or via one of Welker's questions.
At that point, Trump asked Biden whether he was the "big man" referenced in a correspondence that appeared to delineate payouts from the profits of an overseas deal.
"My son has not made money in terms of this thing about what you're talking about [in] China," Biden responded. "I've not had -- the only guy who made money from China is this guy." The former vice president indicated Trump at that point, going on to accuse the president of having a Chinese bank account.
Trump replied that the Biden family are collectively "like a vacuum cleaner sucking up money."
In addition, Baier said the president effectively used Biden's long tenure in Washington against him, pointing to the decades between the candidate's 1972 election upset of Sen. J. Cale Boggs, R-Del., and the end of his tenure as vice president in 2017.
"He did that very effectively. In fact, the Trump campaign put out a statement afterward, and that's what they led with: that he unmasked Joe Biden as a typical Washington politician who was 'all talk and no action'," said Baier.
During the debate, Biden dismissed Trump's claims about his tenure being corrupt as "malarkey" and responded that the forum should focus on everyday American families and not his or the president's.