Jonathon, what you're saying about adverbs not being a predictor of poor quality writing probably is true in the abstract. But, like Brinestone, I have read and critiqued a lot of amateur writing in the last few years (I'll add here that I consider myself to still be an amateur, although a more knowledgeable one than a few years ago). In actual practice, over-use of adverbs (specifically -ly ones, as Brinestone noted) is so common amongst beginning writers that it is actually a predictor.
Back to the mole analogy, if you just thought that a mole was a mole, you wouldn't be able to predict cancer by examining them. However, if you've learned through experience or training that some kinds of moles are usually bad news, they become much more useful. So, someone who has had the experience of reading and critiquing lots of amateur fiction will spot the "bad" adverbs much more easily than someone who doesn't have that experience. That person would also be more likely to scrutinize all adverbs for signs of badness.
Some other fiction writing rules (off the top of my head, based on things I see frequently). These are all things that can be broken if it is absolutely necessary for the story, but there are always consequences. If a writer is skilled enough to handle it, they'll do what they can to minimize the consequences. With luck, only someone trained in the rules will notice, and then only to say, "Hey, look at how this guy broke this rule! And it totally works in this story!"
-Show, don't tell. Personally, I believe that the rule is more correctly stated as "Show what is important and interesting, tell what is important and less interesting, and skip anything that is both unimportant and uninteresting." Example of this rule taken to the extreme: Robert Jordan. However, a lot of new writers do need to learn to write actual scenes instead of just stating what happens, or to show a character being angry rather than saying that he is, etc.
-If you're writing in limited omniscience POV, you can't tell us what non-POV characters are thinking.
-If you're writing in limited omniscience POV, you can't tell us anything that the POV character doesn't know.
-Just use "said," not "remarked, whispered, shouted, etc." Occasional use is fine, but if at all possible, include that information in other ways, like through the actions and thoughts of the character. This goes back to the "show, don't tell" rule.
-Don't hide information that the POV character knows that is important to the story. ESPECIALLY don't taunt the reader by having the character think about the information, but not actually share it. Writers think that hiding information increases suspense, but it really just increases frustration. In some genres this has become so entrenched that it's actually accepted as part of the way you write stories for that genre, but definitely don't use it outside of that genre (it seems like a lot of mystery stories are written this way, although I haven't kept up with the mystery genre so things may have changed). The exception to this is if you have an unreliable narrator, but those can be tricky to handle well.
There are plenty more, but those are broken so frequently that they tend to stay at the top of my mind.
--Mel