In the two films, the main antagonist happens to be someone whose 'nationality' is to the 'opposition' of America in the Revolutionary and Civil Wars. Ian is British and Mitch is from the American South.
Abigail's password is "Valley Forge", which, although somewhat easy to guess, fits with her being a historian and having an interest in George Washington (as witnessed by her collection of the buttons), but Valley Forge might also have special significance to her as a German-American because of its connection to Baron von Steuben.
At the end of the first film, it's revealed that Agent Sadusky is a Freemason, tasked with protecting the Templar Treasure. So when you see him him fidgeting with the spectacles, he's showing Ben how to use them.
In the second film, Ben tells the President that his grandfather acquired the map drawn by George Washington from a descendant of a woman named Charlotte, who was one of Washington's slaves. That would make sense, because his grandfather would still be working on the clue "The secret lies with Charlotte".
In Book of Secrets, Sadusky deploys a team of FBI agents to the Library of Congress as soon as he receives word of Ben supposedly kidnapping the president, coyly remarking that "maybe he wants to check out a book"—meaning that he knows the location of the titular journal. Since the book is supposed to be "by presidents, for presidents," this seems odd, until you realize that several presidents have been assassinated during their time in the White House, and others have died abruptly. Naturally there needs to be some failsafe for those occasions; it's likely protocol that the president entrusts at least one other person with the knowledge of the journal's hiding place in the unlikely event that they aren't able to pass the information off to the president-elect after their term is up. Sadusky, given his status as a Freemason, is a natural choice for the job.
In the second film, when Ben takes the president through the secret tunnel at Mount Vernon, the levers to get inside are covered in undisturbed dirt and dust. This means that Ben didn't test it out before he took the president down there. He had no way to know that that tunnel was still safe for them to walk through, hadn't collapsed, wasn't full of rabid raccoons or something, etc. Kidnapping the president was one thing; potentially accidentally getting the president (and himself) killed in said kidnapping is another thing entirely. Thomas Gates's fallen reputation would have wound up being the least of the Gates family's problems.
Also in Book of Secrets - even with Thomas Gates's name officially cleared of any association with the Lincoln assassination, similar real world examples prove there's no guarantee the public will ever be rid of the association between Thomas and the Confederates once it has been put out there. Mitch, even knowing Ben would disprove him, has likely left a black mark on Thomas's name.
