When we talk about something's being a 'bad argument' it's important to keep three things distinct. Unfortunately, we have a bad habit of not doing so, and this ends up messing up how many people talk about fallacies and fallacious reasoning.
The first and most obvious point at which an argument may go bad is in terms of its logical structure. It's important to keep in mind that this is not some logical structure out in a Platonic heaven, but the logical structure of the argument as it is in fact used. An argument that is formally invalid, for instance, only has gone wrong in terms of logical structure if it ought to be valid -- that is, a formally invalid argument can be entirely fine if it is not put forward as if it were formally valid. Obviously all formal fallacies deal with this sort of thing. However, the reverse is not true -- there are fallacies that are not strictly formal that can nonetheless prevent an argument from being well-structured; the most important of these are fallacies of equivocation. They are not strictly formal since they deal with the meaning of the term rather than the structure of the argument; but they mess up formal structure because formal structure requires consistency in the terms.
But arguments are not merely a matter of structure, and even a well-structured argument may be a bad argument. The reason is that you are not just putting arguments out there and contemplating them; you are trying to do things with them -- make a point, persuade, refute, whatever. This is a practical question, and practical questions are questions about means and ends. Whenever you are trying to do something with an argument, the question of competence always arises: is that argument a good means for the end you have in view? Most fallacies on this question are fallacies of irrelevance, but, again, the reverse is not true. Indeed, one of the most striking cases of an ineffective argument (as we might call it) can be both formally flawless and entirely relevant to the topic at hand, namely, the fallacy of petitio principii or begging the question.
But practical matters are never merely matters of competence; if you can ask whether the means are good means for their ends, you can ask whether the ends are good ends in the first place. Thus the ethical question arises. A good example of a fallacy that is ethical in character is what is usually known as 'poisoning the well'. Indeed, its origins are entirely ethical. Kingsley had insinuated that Newman lacked that all-important English virtue, 'candour'; Newman's reply used the image of an army poisoning the well, to suggest that the sort of insinuation in which Kingsley was engaging was itself less than fair and candid.
It is clear that we are often not clear about which of these is in play. When we accuse someone of a 'straw man fallacy', for instance, it is often difficult to say whether we are accusing them of arguing ineffectively or arguingly deceitfully. Indeed, it seems to me that most people make the most they can of the ambiguity, officially only criticizing the appropriateness of the argument the other person set up to destroy, but still insinuating at every turn that the other person is dishonestly trying to pull a fast one. Needless to say, this is not always a naive confusion, and at least sometimes is a clear case of dishonesty itself.
There is also a bad habit -- a very, very bad habit -- of treating questions of competence and ethical behavior as if they were somehow logical questions. Thus an argument is accused of an 'ad hominem' fallacy, and this is treated as somehow a feature intrinsic to the very character of the argument as an argument. But if the logical features of the argument trace out its flesh and bones, the practical and ethical features trace out its life and behavior. They are distinct questions. The same behavior that may vitiate an argument in one context might not in another context, if circumstances have changed enough to change the standards of ethical evaluation.
Given all this we can propose a better way of distributing fallacies than we usually get:
(1) pertaining to flaws in the argument as considered in itself
(1a) formal/structural: formal fallacies, e.g., denying the antecedent
(1b) material/terminal: fallacies of equivocation
(2) pertaining to flaws in the argument insofar as it is a means to an end
(2a) involving irrelevance: forms of ignoratio elenchi
(2b) relevant but not effective: forms of petitio principii
(3) pertaining to the argument insofar as it is a means to a flawed end
But one could probably do better. I'm not sure that ignoratio elenchi and petitio principii exhaust (2), for instance; false dilemmas are clearly a case of (2), but one might argue that they are not strictly a kind of ignoratio elenchi. (3) can be broken down, but all such methods of analysis seem to be haphazard; I know of no systematic way of doing so.
