The Spanish Empire was bothered by the American Revolution. They gained some previously lost territory from Britain after the war, but their North American allies made them wary of the political and social issues raised during the revolution. They feared that the politics of representation would trickle south and stir up rebellion, which was not uncommon in 1700s Spanish America. They banned texts of American political thinkers and some European enlightenment authors. Thomas Paine, Voltaire, the Declaration of Independence, and copies of the US Constitution were not welcome in the Spanish American colonies, but they made their way there.

One of the larger concerns was that Britain had a powerful military force which could not put down a massed rebellion within an economically weak North America. Spain's military was not nearly as powerful as Britain's and the colonies of New Spain, Peru, New Granada, Rio de la Plata were rather wealthy as far as colonies go. Spain would have to find other ways to put down a rebellion as a placing regular army forces in the Americas would not only be impractical but costly.

The American Revolution no doubt made the royal authorities in the Spanish American colonies take notice of their North American neighbors, but it was the French and Haitian revolutions that helped set off the various movements in Meso and South America. Still, the same literature that influenced and came out of the American Revolution and the development of the United States made its way to France, Haiti, and Spanish America, causing numerous headaches for the royal governments.

EDIT To answer your question more clearly, the American Revolution made other colonial powers wonder if they would be able to prevent rebellions similar to the North American conflict. They began to implement policies to prevent one, but the social and intellectual movements of the time made any such restrictions difficult to maintain.

For an account of how afraid one royalist government was of the spread of revolutionary literature, see Lyman Johnston's Juan Barbarin: The 1795 French Conspiracy in Buenos Aires which is part of Ken Andrien's edited work The Human Tradition in Colonial Latin America.

Also see the chapter "A New World in the Making" in Elliot's Empires of the Atlantic World: Britain and Spain in America, 1492-1830.

I think the summary would be, since were discussing prestige of the British, a simple yes. It was embarrassingly badly managed from stem to stern and reflected poorly on British generalship, military pride etc as well as the poor political savvy of Parliament. It's covered in Frank McLynn "1759: The Year Britain Became Master of the World" which traces the roots of the revolution to the victory in the seven years war; without the threat of French North America in the equation the colonials stopped needing the powerful British military to protect them and so had little reason to wish to keep being deferential to a fairly out of touch Britain.

However, a little "moral high ground" could be held by the British in that they were able to claim it was the continental powers that had defeated her, and not the Colonies.

The newspapers from the time are in some cases available on google books and elsewhere (amusingly some liberal British newspapers published throughout the war actually didn't "support the troops" even remotely) and reading these and their retrospectives after the treaties which concluded the conflict would be useful if you want some contemporary context.

This is a rather difficult question to answer because most primary and secondary sources regarding this topic focus on the birth of the United States rather than the impact the war had on Great Britain. Losing vast amounts of territory can never increase the pride or prestige of an empire, so from that very basic point of view, Britain did take a brief blow. However, if we look at political and economic trends that followed the American War of Independence, we see that Britain emerged from it in many ways as a new nation, ready to build an even more significant empire than she had prior to the war. The results of this war did not impact economic relations between the USA and Great Britain said trade was at a higher level by 1790 than it was before the war.

The war also led to a very generalised militarisation of the British or one could say a strengthening of "Britishness". National identity and local identity increase hand in hand after the war. We also have to look at how the war changed from the onset to the surrender at Yorktown. It beings as a revolt largely focused on the nest of rebellion that was Boston. By the time we reach the early 1780's it has turned into yet another European conflict, where the French, Dutch, and Spanish joined in efforts to tear down the British and their Hessian allies. Here we see that the modern states of France, UK, Netherlands, Belgium, Spain, And Germany were all involved to varying degrees. I could go on about more domestic impacts the war possibly had on British politics and culture but the empire did not falter for long after the embarrassing loss. Britain defeated Napoleon and expanded what would become known as a "Second British Empire". This 19th century empire spread British cultural phenomena around the globe and greatly shaped the world's modern perception of British culture.

A solid source on this topic http://www.history.ac.uk/reviews/review/136