Growing up I was taught that clever brave American patriotic volunteer Minutemen invented skirmishing, terrain cover, guerrilla warfare, sniping, meritocratic/democratic officer selection and used precision rifles while dumb British conscript soldiers led by poncy cowardly nepotistic noble officers wore bright visible red coats and marched in straight lines armed with outdated inaccurate muskets. These claims now strike me as implausible/editorialized, but were there real developments in military thinking/technology that did come out of the war?
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they did not invent skirmishing, I think there was something like that in Frederick the Great's wars being fought a couple decades earlier. Also there were loose french attack formation in the Battle of Plains of Abraham in 1759. Some sort of loose order must have been known. Guerrilla warfare seems to be associated with Rogers Rangers an elite group formed earlier in the 18th century.
However, I do think the rifled musket was probably first used in combat at this time. I believe it was Americans of german heritage so it may have first been a german hunting rifle or rifled musket. I believe the german Jaeger formations were the first to use them in this war.
The first repeating rifle was invented by British officer Patrick Ferguson in 1776 and was used in the American revolution. Ferguson was famously killed in the battle of Kings Mountain, SC. 1780.
The small pox vaccine was invented about this time by Edward Jenner. Washington had his troop inoculated so this may have been the first mass inoculation in history.
Condoms made of some sort of animal intestine also invented about 1776 and I think they were used in america at this time.