At the film's end, Benjamin Franklin checks his pocket watch and its second hand is incrementing in the manner of an electronic quartz movement rather than the smooth manual movement of those times. The quartz watch movement was still 200 years away from invention.
In the 18th Century, men did not wear beards (the exception being some Russians). The upper and middle class gentleman would always be clean-shaven. The poor/laborer classes would only be shaved two or three times a week. Many German soldiers wore mustaches, but neither French nor British (and the colonists were still British) would have worn either mustaches or beards.
When Benjamin Franklin finds the cables being used to detonate the bombs he just lets William follow the wire to find the culprits and stop them. Considering his intelligence the first thing he should have done is cutting all the cables or shorting them to burn themselves.