Well, this is going swimmingly.
It's a smart question, thomas. As is so commonly the case, this term gets tossed around, its range of meanings poorly stipulated if stipulated at all, and because of a bunch of deep cultural reasons, it ends up looking like ages-old flypaper in an abattoir.
If our kid needs brain surgery, we'd probably be happy knowing that surgeon was among the elite in his field. When we dish out the big bucks for a dance or music or theatre performance, we probably aren't hoping for an average performance to unfold that evening. When the US sends a team of diplomats to help work out the Israeli/Palestinian problems, I'd assume we want the elite of that field to be in the team. When we are curious as to some issue of corruption or malfeasance or incompetence in, say, the prosecution of a war in which thousands or hundreds of thousands of people are killed and maimed, we'd probably want (though one never knows, these days) investigations carried out by the very cream of investigators, whether from journalism or from the military or civilian bodies. Regardless whether we might be a German working in Jersey or a governor working in New York, needing a brake job on the Mercedes or a blow job from Mercedes, there seems little in the way of sane reason not to hope for the best that's available.
george's post gets to the real issue here. It's the distinctly American binary opposition between the 'practical man' and the 'intellectual'. American confusion or discomfort with 'experts' reflects the same subject. It's a false dichotomy, wrapped in a few centuries of myth and cultural turmoil and it comes up to us today in precisely the mode he uses the term and in the manner he thinks about this issue.
Missing from all this is the unanswered question of what we mean by "elite".
I think we would all agree that there are indeed standards by which one could judge (with a fair degree of reliability) whether a surgeon or a musician happens to belong to what is currently considered as the elite in his/her respective field. The standards would likely become more the subject of argument if we were to extend our search to include journalists, political analysts, diplomats, or even generals. In these areas the points of view of the observers become increasingly an important factor in the identification - we would discover competing notions regarding membership in these "elites".
In addition, experience teaches us that there are numerous examples of even physicians and musicians who, though widely admired and considered "elite" in their day were later revealed or regarded to be flawed and decidedly 'unelite' by subsequent generations. In short, identification with the elite, even if it can be made without argument, does not guarantee that the subject is truly better at what he does than the average run of humans. This uncertainty is even greater for those categories of human endeavor that don't so easily lend themselves to widespread agreement about such standards.
Finally, one must consider the results achieved by members of various elites. Were they 'good' or 'bad' for those affected by their work - as revealed after the dust settles? Surely Stalin, Hitler, Mao and others would be included in any pantheon of influential 20th century political leaders. However most of us would agree that they caused a great deal of useless suffering - and for no worthwhile end. I concede it is a bit hard to find the right application for a word like "elite" to such figures - prominence in the field and even dominance for a time may not constitute "elite" status to some (even most) observers. However, it is simply a fact that each of these leaders was indeed widely regarded as elite - and more - while they exercised power.
In his last paragraph above, Blatham raises an issue that preoccupies him regarding some peculiarly American (in his view) discomfort with "experts" or "intellectuals" (Hofstadter et. al.), presumably relating that "false dilemma" to my skepticism about "elites". While I acknowledge some connection with his previous arguments on this point, I don't buy it. My reservations are merely those I have stated above, plus a little sympathy for Hans Christian Andersen's ideas expressed in his story about the Emperor's new clothes. They are entirely pragmatic, practical and based on our experience.
I don't exclude the possibility that identification with some "elite" status may also be associated with enduring excellence and beneficial consequences. I merely remind him that "It ain't necessarily so...".