Just wondering what some cons were for the British empire?
Some cons? The British Empire had a lot of things working against it during the Revulotionary War. Historians generally fall into three camps on this question:
For myself, I tend to support the first group and I felt like I should clarify that before we go into detail here.
When the war broke out, the British army was around 48000 men strong. It had recently come out of the seven years war and veteran officers and NCO were relatively abundant, the drawback here was that Britain had incurred a substantial national debt during said war. Another problem was the sale of commissions which allowed inexperienced persons of wealth to buy positions of power within the army.
48 000 was a substantial force, however, 21 of these regiments were stationed in Ireland (which needed a garrison), 7 were in Gibraltar (which really needed a garrison), only 18 regiments were actually in America and 20 in Britain proper.
Another factor that remained problematic for Britain throughout the war was recruitment. Willingness to serve overseas was limited to say the least. Britain was forced to increase the enlistment age to include anyone between 16 and 50 and even pardon criminals in exchange for military service. Morale and discipline was also generally speaking poor in many regular British units.
Throughout the entire war, Britain lacked real allies. Yes, a few minor german states sent men to serve as mercenaries alongside the British but this pales in comparison to France and Spain as allies of the Colonists.
Logistics and supply was difficult for the British, as soon as they needed to move away from the coast or major waterways where they could be supplied by the navy the situation became a real issue.
Delay in orders was of course a problem too, orders issued from Britain were often completely out of date by the time they reached the commanders in America.
When the major European powers of Spain, France and even the Netherlands joined the Revolutionaries the situation quickly worsened for the British, they now needed to keep the lions share of their navy protecting Britain from invasion and also had to divert army resources from the Americas to the protection of both European and other colonial holdings.
Political opposition to the war in Britain was also substantial. The Secretary of State at War was openly opposed to the war. So was roughly half the parliment and many prominent commanders.
Lastly, the very size of the theater always worked against Britain, as the did the largely rural population of the colonies. Even if they won every single battle they fought in a campaign (and they often did), they simply did not have the resources to occupy the land they gained. The British army was designed to fight in Europe, in densely populated areas where wars were often won by marching on a capital, or other significant location of strategic importance, and ending the war in a single decisive blow.
Realistically, had the British army managed to inflict a substantial defeat in -76, it may have dissuaded the other major European powers from siding with the Colonies but after 1777 I personally don't think a victory was ever a realistic possibility for Britain.
Edit: Despite all of this, the war was costly for the Americans and their allies. Battlefield losses, including allies, were around three times as high for the Americans and their allies compared to the British (around 7000 for Britain in all compared to at least 22000 for the Americans and their allies, not including deaths from other related things which may have brought total losses including civilians closer to 70000 for the Americans and their allies).
The biggest weakness the British had was the Atlantic Ocean. Reinforcements, orders and supplies from home could take months to arrive via sailing ship.
When the French and its Navy threw its support behind the Colonies, it suddenly became that much more difficult to keep materiel flowing to the Redcoats.