Off the top of my head:
Clive and I were recently discussing something of this nature, and he pointed out something that I think is worth repeating in this context. The rigor and strength of an argument goes beyond preventing a syntactic error (e.g. violating a basic law of logic or having an incoherent form), instead the more essential features of a strong and rigorous arguments go into preventing the much more complicated realm of semantic errors (A formally valid argument, but contains other, more subtle flaws in reasoning).
A.) I think that several of the informal fallacies are actually trying to get at semantic errors in reasoning, rather than syntactic errors in reasoning. An appeal to authority is a very valid argument, but it's taking on board several important, unexplained (and, in some instances, incorrect --it depends on the "expert") premises.
1.) The expert actually has a knowledge exceeding that of the laypersons on the subject.
2.) If asked to a give a proof, the expert can, in fact, give the evidence and the reasoning supporting their opinions, and this proof will be both valid and warranted (i.e. a sound argument).
3.) I think the part that's missed here is that an expert opinion is worth much less than a consensus opinion (i.e. getting a bunch of experts together and getting an overwhelming majority opinion, e.g. like 95% of them agree about proposition X). Strictly speaking, you should take a consensus opinion over an expert opinion every time. (This means collections of well-cited scientific papers with many proponents in the scientific community.)
So appealing to an expert is more about having well-founded or warranted premises than making an entirely self-contained valid argument (Of which none, outside of math, really exist). However, if any one of the premises listed above aren't true, then it's the appeal to authority is basically, by definition, a false appeal to a false authority, which is a fallacy.
B.) As stated, semantic errors aren't about logical form. So, yeah, everyone can agree upon "If A, then B. A. Therefore, B.", unless they're extremely green at logic. The subtle question, however, is "Why do you think A is a warranted assumption?" and "What warrants you to think that A and B are correlated in such a manner?" Essentially, this is why making a valid argument is such a low, low bar at some level. If you can stop yourself from making the trivial syntactic errors, you're still leaving yourself wide open to the vast array of semantic errors. The premises "If A, then B" and "A" are usually subject to inductive reasoning (probabilistic arguments) and abductive reasoning (intuitive reasoning), and those are often non-trivial to evaluate and understand.
The appeal to an authority is placing some trust in (1.)-(3.) above, but if that person is actually an expert, then there's good reason to suspect that they will be garbage handling at least some of the semantic errors for you. In other words, they'll be part of a community that hopefully has been confronted with and come up with effective methods of dealing with probability theory, honing their intuitions, understanding how to reason about issues related to A and B, they'll have an advanced network of knowledge about facts related to A and B, and so on. Therefore, all things being equal, they'll give more reliable premises to start your arguments from than people who don't have experience on the subject matter. But here the criterion is having reasonabe, reliable arguments, not having verified, 100% true facts of the matter.