Great can mean so many things. The Roman Empire was great, then it collapsed and no one even knew it for many decades. So, yes, I would assume America can still be considered great. There is a plethora of things that America is not however and that to me is the problem, not our greatness.
Yes, I agree that America is still a great country in today's global society, because people will always hate America as long as we are so successful. The only problem with America is that our government appears to have turned on us. But America is still strong. And what America stands for is still relevant and worth holding on to.
If the current massive migration from North Central America and the Caribbean keeps going at the same pace it will turn this country into replicas of those places...Limited immigration is needed as its already set up to be. Excess of anything is toxic, immigration is no different. Too many immigrants and immigrants will replicate their former homes over here, like is already happening.
The United States is still a wonderful country. The modern era has shown other countries becoming democracies or developing democracies, but the United States still stands as a special country. It was founded on freedom of religion and on personal rights. It was founded on the people leading, rather than on a monarchy rule. One of the most important things the U.S. was founded on--that other countries still look upon with favor--is that it is a country of immigrants.
I believe that the US government has had some serious missteps with the last few presidents and governing bodies and I do believe that we are in worse shape than we have been in the past. With that said, there are still many things that our country does right and we still have a very workable society, therefore I would still consider it a great country in comparison.
This is not to say that the United States is not the easiest country to live in because it is. But in today's global society, the United States as a power is not leading, and it isn't certain that it should be. It is an equal player with many of the world's leading powers.