This may not be the most popular answer with the current pro-american sentiments but I am going to say nothing. Nothing was remarkable about the British army, at least not in any way that had a positive impact on its preformance in the american war for independence.

If anything the British army entered the war weaker than it had been in a long time. Britain had just come out of the seven years war and while it had been victorious, it had not been a good victory. Most of her allies were war weary and more importantly, they were continental allies without strong navies or colonial holdings.

At 48 000 men the British army was stretched thin indeed. Ireland needed a strong garrison lest the Irish catholics got ideas and started conspiring with France. Again. Gibraltar needed a garrison lest the King of Spain got any radical ideas like "Maybe Britain doesn't deserve to hold the most strategically important rock in Spain?" and so on.

Added to this the seven years war had been bloody expensive for Britain. The country was in debt. Most people, including a very significant part of the ruling class, were very unwilling to enter another costly war. Britain was tired of bleeding blood and gold. In part to alleviate some of this, the sale of commissions was permitted, this brought in money and enthusiastic officers, sadly they were very often the wrong kind of officers.

See, one of very few thing Britain had going for it was an experience core of veteran officers and NCOs who had been through the seven years war. Sadly the sale of commissions often displaced these generally competent men with incompetent replacements, squandering the one small advantage the war had brought.

To further compound the problems faced by Britain their army was never intended for a war in vast theaters. The British army was good at what it did, a swift advance against a key objective in continental Europe. The distance is another often discussed factor. Reinforcements, orders, supplies, everything took time to reach the americas, something that was only possible in the first place thanks to the British Navy. The supply situation in the colonies was even worse. Whenever the army could not be supplied by the navy problems occurred almost instantly.

Recruitment was difficult for the British before the war and became a downright nightmare during the war. Enlistment age was expanded to anyone between 16 and 50 and petty criminals were pardoned in exchange for service. This was not an enthusiastic body of men and when led by incompetent officers into a war that lacked solid support at home... well.

The american war for independence is often portrayed as a David vs. Goliath story, especially in American circles. I am not so sure I agree. It almost certainly seemed that way to the Colonials at the time but I find it very difficult to see that a British victory was even remotely possible after 1776.

In either case the answer to your question is perhaps not unlike that of the front page post. The remarkable thing is the resilience displayed by the British army. Their ability to carry on a war for year after year with poor supplies, harsh discipline, poor morale and increasingly alone in one of the first true global conflicts.