Most law school exams, to my knowledge, involve a single end-of-semester exam. Some comments in this thread argue that this is pedagogically unsound, and that having several exams — a final plus a midterm or two — would better measure people's knowledge. (It might also help students learn the material better.) I'm not sure that this is so, because I haven't looked into the research; but it seems plausible, and colleagues I trust have said that the research does support this. Let's assume then that this is right. Why then the single-exam format?
Some of the commenters identified one important answer: Professors hate grading exams, and would thus rather grade one exam than two or more (since presumably the two or more put together would involve more pages of exam answers than just the one). With few if any exceptions, law professors do all the grading themselves. "Law is the only discipline in which students select what's published in the journals and the professors grade the exams." Professors and professor-run bodies get to decide how many exams there'll be. Professors hate grading the exams. You get the picture.
I think there's a lot of truth to this, but let me suggest an extra factor: I suspect that most students prefer the one-exam structure as well, so that there's little pushback against the professors' one-exam preference, and there would likely be some pushback against professors' attempts to shift to the "better" two- or three-exam format.
In my experience, most law students are very serious about studying for exams, and thus spend a lot of time studying for them and stressing out over them. What's more, if you cut the significance of the exam in half, students won't think they have to study half as long or half as hard. Rather, they'll still see themselves as in hot competition with the other students, and will feel the pressure to study nearly as hard and long for each of the two exams as they would have for the one.
Naturally, some students might value the greater accuracy of the multi-exam approach, and the lower risk to them that this approach provides (since they don't need to worry as much about tanking a class because they screw up one exam). But for many students the downside of yet more studying and yet more worrying exceeds the upside of less risk and better measurement accuracy. And on top of that, grades are on balance mostly a zero-sum game — more accuracy of testing will just rearrange the As, Bs, and Cs, so as many students will lose as will win. Increased time needed to study for exams is a net loss for students as a whole. Therefore, you'd expect that more accurate measurement devices will please only a few students, while greater need to study will displease many more students.
So professors don't want to institute more exams, even if having more exams provides more accurate measurement. More students, I suspect, don't want to institute more exams, even if having more exams provides more accurate measurement. Who would predictably benefit from more accurate measurement, and lose nothing from it? Employers, and perhaps indirectly the legal system generally.
Employer pressure may indeed have some broad effects. For instance, while abolishing grades would make life easier for professors and would in some ways make it easier for students, most employers won't hire students who don't have grades. Even Yale, which some say "doesn't have grades" does have a "High Pass" and a "Pass" [UPDATE: and two lower grades which are rarely given], which selective employers definitely focus on; and schools that aren't as selective as Yale probably couldn't get away even with that (though Berkeley somehow manages with only three grades).
But on balance I suspect that few employers care about precision enough to make a stink about this. The grades give employers some decent signal of applicant quality; employers realize that no grading system would yield a perfect signal; it's hard to tell how much extra accuracy one grading system provides over another; the random noise in the grading probably averages out in considerable measure when you look at the student's entire transcript; so employers are unlikely to spend much time and effort on even thinking about the midterms-or-no-midterms question, much less trying to pressure stodgy academic institutions into changing their ways, or shifting their hiring practices towards schools that provide more midterms (which would provide indirect pressure on the law schools).
This is just a casual analysis, not based on any deep thought, and I might well be mistaken. Yet it seems to me that while professor self-interest is an important factor here (a free-market guy like me must surely appreciate the importance of self-interest in molding human behavior), student self-interest may in practice reinforce the professor self-interest rather than clashing with it.