Despite having one of the largest and best-trained fighting forces in the world, the British military did indeed commit a number of grievous blunders that led to its defeat in the American War of Independence. There are many blunders that you might consider in addition to the ones described below.
Early on, the British tacticians assumed that their military would simply be able to intimidate the revolutionaries into defeat. For instance, at the Battle of Bunker Hill on June 17, 1775, British forces marched shoulder to shoulder against a lightly fortified entrenchment of colonial forces. They assumed that their enemy would break and run when faced with the prospect of standing up to the well-disciplined British army. Instead, the colonials found themselves presented with a larger target, stood their ground, and inflicted heavy casualties until they began to run out of ammunition. The British were eventually able to take the hill, but not until they shifted their formations by advancing in single-file lines to present smaller targets. This particular battle was very costly for the British, resulting in over one thousand casualties. Throughout the war, similar instances of the British deploying their troops with the intent to intimidate failed to achieve their desired effects.
The British also made errors in choosing where to deploy their armies throughout the colonies. Early on, they hoped to isolate the revolutionaries in New England and focused their forces in the northeast. British strategists did not grasp the severity of the rebellion or how quickly revolutionary sentiment had spread throughout the colonies. Once other colonists joined the cause, the British found themselves in need of making hasty and at times disorganized redeployments elsewhere.
Sometimes the British focused on capturing and occupying the wrong places in their misguided attempt to replicate European military strategies in North America. Often, they were more concerned with holding land than pursuing the enemy. For example, British forces were successfully able to occupy New York City and the Hudson River Valley as part of their plan to isolate New England. But by doing this, they failed to pursue Washington's already weakened army as it fled further south to regroup.
Similarly, General Howe thought that by capturing Philidelphia, the de facto colonial capital at the time, he could force the revolutionaries to surrender. Such a strategy may have worked in Europe. Instead, it left the British army further north without support, leading to their humiliating defeat at Saratoga. Furthermore, rather than capitulating, colonial forces in Pennsylvania merely retreated into the countryside, where they continued to fight.