Eh, no more than anyone else in the world. Your average european knows about as much about Venezuela as your average american does. Most people from Japan can't find Kenya on a map, either.
When it comes to the world stage and knowlege thereof- the average person knows about two countries in any detail. The first is their own native land. The second is america. An "educated" individual, of any nation, will also know about other big hitters- such as the UK, Japan, China, India, Russia and of course whichever bits of the middle east are being a pain this decade.
Beyond that, basically everyone is as badly uninformed as average americans, and often times misinformed in ways that we're not.
National prejudices are still alive and well in most of the world. America... not so much. I don't pretend that's out of any kind of virtue on our part. But prejudice requires we care in the first place.
And then one has to come to terms with the scale of America, as a nation.
America: 3.79 million square miles; 312 million people; 52 major political zones (counting D.C., clumping the island chains as "one"- and leaving out midway since it's basically hawaii)
Europe: 3.83 million square miles; 857 million people; 57 major political zones (counting things like Vatican City and Gibralter)
We are close- but not quite- on par with all of europe combined in terms of complexity. Less population density, for sure. This spread does include Alaska... and a chunk of mostly unused Russia. So while it's not "even", it's "close as it's gonna get".
And culturally speaking, yeah... we are a mess. At least europe has nice, clean boundaries to determine who does what, and where they go to do it. Is it any surprise our country's so messed up? Texans have to listen to the opinion of Alaskans and Hawaiians and New Yorkers. When a single change is instituted in any state in our union, the whole country has to adjust.
When was the last time Great Britain had to change their policies and laws based upon a vote in Latvia?
Any knowlege of america should be treated as equivilent to all knowlege of europe. Every state, a nation unto itself.
And when we get to that kind of scale... everyone's poorly educated and ignorant... not that I'm saying I exactly approve of this fact. If anything, it scares the piss out of me. But it's a HUMAN flaw. Not an American one.
On the other hand... well... our education system is shot to crap. It's a significant problem. But given, again, america's... complexities... it's not terribly surprising. Would europe do any better if the combined total of it tried to function as one nation? Signs point to "hell no". Just look at the recent disaster with Greece and what that did to the Euro. And then multiply that by a factor of every other poor and mismanaged nation in europe.
That's what America has to deal with. All. The. Time.