A few observations on things that interested me:
+British society was very corrupt and 'dissolute' at this time. Some people say the same thing about the US today. That was, in fact, one reason often cited for independence.
+ This is a little bit of a tangent, but the US today is not an 'empire' like Britain was, nor do we have 'colonies' like they did. As Tom often says, 'empire' is about enforcing maximal rule-sets. We encourage and promote minimal rule-sets and enforce hardly any. Sure, if you want to be in the WTO, you have to open up some of your banks, but that's not 'empire'.
Some people want to say that our military are 'imperial grunts'. That's only true if you call 'making the world safe for capitalism/globalization' 'empire'.
+ Military men generally believed that New York (City) could not be held without naval superiority, which the colonists most certainly did not have. But they still tried to hold it and got creamed. The Birtish took Long Island, then Brooklyn, then New York (Manhattan) island, then Fort Washington, the Fort Lee. Not smart.
+ The British and Hessians could not believe the prosperity of the Colonies, even after places like Long Island had been partially destroyed by the retreating colonists. 'Americans in 1776 enjoyed a higher standard of living than any people in the world.' The abundance of America made the British soldiers who saw it feel even more that the rebellion against God's appointed King was even more unjustified.
+The British, and especially the Hessians, earned a lot of ill will by pillaging and raping.
+ A very important American retreat took place on my birthday! We all know Washington crossed the Delaware on Christmas, 1776. 'Surprised the Hessians in their lair' (to quote Schoolhouse Rock ;-). Washington crossed back to Pennsylvania, then crossed back to Trenton to hold against Cornwallis. January 2nd, 1777 is called the Second Battle of Trenton, though, as I said, it was more of a calculated retreat. The Continental Army held Trenton until nightfall, then retreated south under cover of darkness.
The Americans left a token force to build fortifications as though they were planning to defend at the creek, and to disguise the sound of their march. British forces perceived the movement, but Cornwallis believed this to be Americans planning a night attack, and thus ordered British troops into defensive positions, allowing Americans to succesfully march their army around Cornwallis and start the Battle of Princeton.
Since the Battle of Princeton was on January 3rd, you know that was the future birthday of Professor Tolkien, right? ;-)
The army quick-marched east and then north to Princeton, literally wearing rags and often without shoes. They beat Cornwallis' rear-guard there, many of whom were on the way west to Trenton to join Cornwallis. By the time Cornwallis got there the Continental Army had retreated north to Somerset. The First and Second Battles of Trenton and the Battle of Princeton were mostly important victories for the morale of the army and the country.