Brian63 has convinced me that the argument from expertise is not necessary fallacious. It is possible to understand and believe a statement such as "The Earth is 4.5 billion years old" without understanding, even in principle, the actual scientific justification for this belief.
(Chris Hallquist has also been tracking this subject.)
I still don't like the argument from expertise.
While it's not necessarily fallacious, it can be fallacious in the manner I describe earlier. It seems difficult if not impossible to understand a statement such as "light is both a particle and a wave" without understanding its justification. This fallacy is especially applicable to statements about God, especially philosophers' statements. What a philosopher means by "God" is quite often "the sort of being justified by argument X". The "God" established by Plantinga's modal argument is very different from the "God" established by Aquinas' arguments, which is very different from the character depicted in Christian scriptures.
It's very easy to misconstrue an argument from expertise as an argument from authority. Arguments from "true" authority are typically sound: Catholic doctrine is what the Pope says it is; the Constitution means what the Supreme Court says it means, the defendant is legally guilty or not guilty according to what the jury declares.
The problem is exacerbated in the sciences because scientists are authorities on what science says, but they are merely experts about how the universe actually works. The conflation between authority and expertise crops up all the time in discussions of evolution: Cretinists often misrepresent what science says, or argue that they should have equal authority to declare what science says, often arguing that the lack of perfection entailed by scientists' mere expertise about how the universe actually works undermines their authority to establish what science says.
Most importantly, though, the argument from expertise is lazy. Laziness is all right, I suppose, when you don't care much for some topic (I really don't care whether the Earth is 4.5 billion years old, or 3 billion, or 6 billion), but if you don't care about the topic, why should you care enough to bother to argue the point?
When you do care about a topic, however, the argument from expertise is inexcusably lazy. The vast majority of most experts' training is in how to do original work in their field. But lay people don't need to do original work, we need only to understand the work actually completed. If you want to understand the arguments establishing the age of the Earth at 4.5 billion years, all you have to do is go to Talk.Origins, search "age of the earth", and read for a couple of hours. To understand an argument it takes only a minuscule fraction of the time it did to construct the argument.
There are fields (e.g. quantum mechanics) where understanding the justification takes considerable work. However, it is precisely these fields where it is difficult to understand the proposition (e.g. light is a particle and a wave) without understanding the justification, i.e. where the argument from expertise is indeed fallacious.
The argument from expertise is dodgy, has pitfalls, can be fallacious, and even when it works it saves the reader only a trivial amount of time. Who can say anything good about this argument?