I can at least provide some context for this question if not as complete an answer as you might like. As to the second part of the question, whether citizens or subjects of other nations had opinions running counter to their leaders, I don't believe I'm in a great position to answer, except perhaps in the case of Britain, the non-US country whose politics with which I'm most familiar.

For one thing, we should state one fact of significance: this expansionist policy was not unusual, so it would not necessarily have been looked on as remarkable at the time to foreign observers, either in a contemporary or a historical sense. It would not even necessarily have been out of character for republics to engage in conquest to expand their territories, as both democratic Athens and republican Rome had been aggressively expansionist in their policies. Nonetheless, military expansion was seen under the conventional wisdom of popular history as being dangerous to the fortunes of republican governance, as it tended to produce an appetite for militarism and political generals who might overthrow the very system they had served (for many in the US intelligentsia in particular, this was the "lesson of history" to be applied to figures ranging from Caesar to Napoleon). Nonetheless, realpolitik of the day demanded an expansionist policy for the United States, though there was disagreement on how best to pursue it, a major point of contention between Democrats (particularly Southerners) and Whigs by the mid-19th century. It's also worth noting that the 19th century, particularly the latter half, was the era of new imperialism for European powers, as Britain, France, and other nations seized territory in Africa, Asia, Oceania, and elsewhere. Britain claimed more direct control of much of India, for example, in 1858, after using the East India Company as a proxy for several decades. Both Russia and China aggressively attempted to develop their hinterlands--Central Asia and Siberia for the Russians, western territories like the Tarim Basin and Xinjiang for the Qing Dynasty--where they had extensive land claims, but little actual power of governance and enforcement, and deals with local leaders of "outside" ethnicities were common (including Kazakhs, Turkmen, Uighurs, etc). New technologies (especially gunpowder) and state leverage allowed for centralized control of these regions in a similar manner to how the US "pacified" its interior Native peoples--and often with a similar level of brutality. So many of the rest of the world's leaders would not have looked askance at American expansion or viewed it as hypocritical. [1]

Let me take a more specific set of incidents with which I'm most familiar, from relatively early in the 19th century: the formation of the Monroe Doctrine, which set the stage for American expansionism in the western hemisphere for much of the remaining century. By the close of the French Revolutionary and Napoleonic Wars, Spain had weakened considerably and its grip on its western hemisphere possessions grew ever more tenuous. Under significant pressure, and military dealings of dubious legality on the part of Andrew Jackson, Spain was persuaded to sell its Florida possessions to the US. The Spanish ambassador, however, slyly included provisions that would have allowed private land grants in Florida to remain controlled by Spanish owners, and prior to the ratification of the Adams-Onis treaty, the Spanish crown issued extensive land grants to court favorites of the Bourbon monarch, Ferdinand VII, that would have left much of Florida under Spanish control. Only after further pressure and ongoing revolution in the western hemisphere was Spain persuaded to nullify these grants, as it was clear the US was likely to ignore them anyway. Monroe and Adams issued the statements that would become the "Monroe Doctrine" in 1823, declaring the New World "off limits" for further European colonization and forbidding Spain from transferring any imperial holdings to any other country. Britain, for its part, had already planned on issuing a similar edict, and unlike the US, it had the naval clout to back up its threats. For these reasons, with a few notable exceptions, American and British foreign policy were in harmony for much of the 19th and early 20th centuries, at least regarding the Western hemisphere. On the Pacific Coast, Russia attempted to exert additional sovereignty by warning Spanish (later Mexican), American, and British mariners to avoid its North American holdings in what is now Alaska and parts of the Yukon. Both Britain and the United States came to separate understandings with the Russian Empire, and for a time, US relations with Russia were probably warmer than with any other European country, save perhaps Britain. A problem emerged, however, in that the Russo-American agreement marked the southern bound of Russia's claim at 54°40′N, and the Anglo-American agreement on Canadian borders fixed their border at 42°, leaving the intermediate area subject to dispute (hence the slogan of bellicose Democrats in 1844, "54-40 or fight!") until an agreement was reached during the Polk administration concerning the Oregon territory--it will be remembered that the Polk administration also saw the most aggressive war of expansion undertaken by the United States to that point, when it invaded and captured the northern half of then-Mexico. After the Civil War, the US pressed the Monroe Doctrine to persuade France to cease military support for the Habsburg emperor Maximilian's ill-fated conquest of Mexico as well, the first time it had to be explicitly asserted to a European power. [2]

Near the end of the century, the US again embarked on a serious campaign of expansion in the Spanish-American War, near the zenith of European imperial power in Africa and Asia. As the US prepared to take control of the Philippines, Cuba, Puerto Rico, and Guam, US Senator Albert Beveridge remarked, " God has not been preparing the English-speaking and Teutonic peoples for a thousand years for nothing but vain and idle self-admiration. No... He has made us adept in government that we may administer government among savage and senile peoples....He has marked the American people as His chosen nation to finally lead in the redemption of the world…" His statements, shockingly racist though they are today, were not seen as out of character for either American nor British elites. Indeed, Rudyard Kipling a year earlier wrote an ode to American expansion, famously urging them to take up "The White Man's Burden" to develop and "civilize" other parts of the world. Unsurprisingly, the zenith of the age of imperialism was also the zenith of what we can term "scientific racism," under which white supremacy was taken as an article of biology, and "race" was very much a term of social scientific art. Under this context, American hegemony over its own black citizens, "aboriginal" peoples of the First Nations, and newly-acquired people of color in Latin America and the Philippines would not have been seen as unusual by the principal powers of Europe, who were occupied with their own colonial projects. [3]

So the short answer is that some nations certainly contested American expansion when it conflicted with their own interests--as we've seen in the examples of Spain, Mexico, Britain, France, and Russia--but they did not necessarily view American expansion as "unusual" or unexpected.

References and further reading:

[1] Stephen Howe, Empire: A Very Short Introduction

[2] Daniel Walker Howe (no relation), What Hath God Wrought: The Transformation of America 1815-1848

[3] H.W. Brands, American Colossus