Lest any modern straight (and sometimes bleached) teeth appear on camera, every last extra in the cheering crowd at George Washington's inauguration got their teeth painted with special fast-drying saliva-proof "gunk" paint. Working-class characters were given proportionately worse-looking smiles than the merchants and aristocrats.
During George Washington's inauguration, the apparent cheering crowd of thousands was actually filmed with only around 80 people. They would stand in a square formation - edged by green screen cloth. After filming a few seconds of giddy flag-waving, the 80 would switch positions, trade flags and buntings around, pick up different things (pitchforks, tankards, children, etc) and move over thirty feet. The process was then repeated numerous times. By day's end, there were enough squares of different-looking crowd activity to stitch the lot together digitally and make it look like a seamless mob of thousands.
When David McCullough (writer) met Paul Giamatti for the first time out of character, he did not recognize him as the actor who played John Adams.
During an interview on NPR's "Fresh Air," Paul Giamatti told interviewer Dave Davies that the scene in which Abigail and John have sex upon being reunited after many years apart was not written as a sex scene. The script only called for John and Abigail to kiss, but Giamatti said that he and Laura Linney discussed between themselves that they thought the characters would go farther in that situation, and they decided to "keep going" and hope the director and camera person would follow them, which they did. The scene they improvised and shot was originally much longer than what ended up in the finished film.
History buffs might recall that a British Navy surgeon concluded (shortly before 1750) that sailors could reduce the incidence of painful and debilitating scurvy by sucking on limes. Concurrent experiments involving sailors taking vinegar or sea water failed. Eighteenth century medicine was unaware that limes contained Vitamin C (a substance not really understood until the 1930s) and also did not fully comprehend scurvy as a nutritional disease, but crews were issued limes in their rations after the field study. British sailors and later British people generally were nicknamed "limeys" shortly afterward. At the film's dock set, around a peck of sucked-on cut limes litter the ground as if discarded by sailors.