This is an interesting question.

Erik Goldman and Anirudh Joshi basically using the question to make a rather cynical comment about the state of physics today (physicists turning to superficial Internet entrepreneurship and finance).

Richard Tabassi seems to be treating Einstein as merely an iconic "leading physicist" and is mapping him to a bunch of usual suspect questions.

But let's consider the relevant facts about the personality of the guy. I am not actually super well-informed about his life and biography, but I'll indicate roughly the way to think about this question in a way that reflects the real personality of the real Einstein, not Einstein as poster physicist or Einstein as Symbol of the State of Physics.

Let's take a serious shot at profiling.

1. He was extremely creative and had startlingly unusual perspectives on things. His talent lay in coming at things from completely weird angles. Angles that others would never have thought of.
2. He worked in a patent office and only later in life worked in "famous" settings. He was nothing like a careerist (though you shouldn't read too much into the patent office thing... he was not an "outsider" to the physics establishment or anything that romantic, but he was definitely more of a backwaters guy than an academic careerist winning big grants and young-genius chairs like modern young TEDdy hotshots... in America today, he'd be teaching at a community college somewhere rather than MIT or Berkeley).
3. He wasn't particularly good at math compared to his peers whose work he built on and who built on his work. He relied a lot on collaborators to help with the math. Much better than you and me, but not great. His contributions came from originality, not technical skill.
4. He had a philosophical bent of mind, but was not primarily a philosopher. He was more of a folksy wisdom kinda guy. A Yogi Berra for physics. Compared to truly philosophical physicists like Murray Gell-Mann, he was basically uninterested in philosophy as far as I can tell.
5. He once said that his secret was pondering childlike questions about space and time as an adult, when he could actually do something about them. That tells us he had a natural inclination towards fundamental things and a child-like sense of priorities.
6. By all accounts he appears to have been a very simple man in his lifestyle who valued his leisure and time for extended deep contemplation (anecdotes like the one about using the same soap for shaving and bathing, , shaggy hair, talking long walks, eating ice cream...).
7. Unlike other types of geniuses like Paul Erdos for instance, he did not publish thousands of small brilliant things. He published two major theoretical contributions and a bunch of others, but he was not prolific in any numbers-game sense of the term.
8. He's on record as having made that very revealing remark that he'd rather be a plumber than a professional physicist. Suggests how self-aware he was about the nature of his own talent and why it was effective.
9. We have to be wary about assuming he'd be equally good at social science. He is on record making that remark that "politics is harder than physics" so he clearly appreciated the problems. But I get the sense that his thinking was still primarily mathematical (geometric in particular). I doubt he'd be interested in non-mathematical subjects and purely qualitative, messy methods.
10. The one big unknown is how he might have related to computers and computing. I genuinely don't know how to think about this. I'd be curious if others have good ideas. I suspect he'd have been a Dennis Ritchie type guy in CS: make an important fundamental contribution that shifts computing paradigms without being voluminous in terms of lines of code, but not necessarily hugely prolific and productive consistently.

These traits do NOT map to becoming a finance quant. Or an ad targeting. Those would actually require vastly more energy AND complicated technical proficiency AND a singular lack of aesthetic sensibilities AND a sort of worldly interest in money/visible success that I doubt he had.

The profile does not fit.

The traits also do not map to some usual suspects list of questions. The problems outlined by Richard Tabassi represent a very different era of physics: one of gazillion dollar experiments, hugely complicated and intricate mathematical theories, etc. We are in a state where some people think of Superstring theory as almost a religion and "not even wrong." These represent a state of physics that is either:

1. An "end of physics" state where we can no longer answer the questions we can pose. John Horgan has argued this point of view nicely in his book The End of Science. If so, we're in an angels-on-pinhead state of "ironic science."
2. The cusp of a paradigm shift like the one that existed around the idea of "ether" just before the Michelson-Morley experiment
   
   

Assuming optimistically that we're in the second kind of state, an Einstein type personality will actually not be able to contribute anything until the current paradigm is "broken" by something like the M-M experiment, creating a radically unexpected situation/paradox that requires someone of his talents to put humpty-dumpty together again.

This situation favors heavy-lift theoretical systemizers (Edward Witten, J. C. Maxwell, Poincare) with formidable synthetic powers but not necessarily a talent for surprising shifts in perspective or paradox-resolution.

I mean think about it: an idea like "maybe the speed of light is constant for all observers" is just so completely weird and out of left field that it doesn't really come from skill, training, education etc.

This is the sort of guy who comes in after everything has been devastated by a paradigm failure, and comes up with a new way to put the pieces together. Things aren't exactly working well now, but they aren't shattered.

So physics is not actually in a favorable state for an Einstein type personality to do big things. Maybe in 20-30 years if an unexpected experimental result emerges from CERN or somewhere that topples the current models.

So is there some other field of human endeavor that would reward an Einstein?

I think one possibility is nailing the connection between computing and physics.

Another might be making a genuine advance in computational complexity. Possibly casting P != NP in a surprising new light that breaks the impasse of understanding/insight there.

A third might be coming up with a true theory of complex networks (scale free graphs and all that sort of thing). Right now, that stuff is a sort of Keplerian-empiricist state.

But basically, it is completely unpredictable. What is interesting about the Einsteins of history is that they force very sharp turns in our thinking that we cannot predict before the fact. That's why they're called "paradigm shifts."

By definition an Einstein is someone who asks the right question rather than answering questions assumed to be the right one.

If I could REALLY predict what question an Einstein would work on, I'd be that Einstein.