non quidem est dubium quin ceteros duces aspernandi causa hoc dixerit...
"There is indeed no doubt that he said this in order to upset the other generals."
You could translate it thus, but a (somewhat less desirable) alternative is possible:
"There is indeed no doubt whether he said this in order to upset the other generals."
When there is no doubt whether something happened, the conversational implicature is, in most contexts, that it did happen. This applies to most languages I know. Even so, whether... is an indirect question, not a mere declarative content clause (which would usually be expressed in an a.c.i.). Indirect questions normally require the subjunctive mood. So this suggests to me why it is considered an indirect question.
In general, indirect declarative clauses are expressed in the a.c.i (although I'm sure there are exceptions, which I will ignore for the moment...). By an indirect declarative clause, I mean that the speaker does not express his modal attitude towards the content of the clause: he does not say explicitly whether it is desirable, nor whether it is probable. This usually means it is presented as a plain fact. The word "doubt", however, strongly suggests an attitude about probability.
One might think the word non cancels this attitude; but, in practice, it does not; it's merely considered by Romans to be an extra modifier to the doubt—or that is how I have always interpreted this use—just as we can still use there is no doubt whether in English even though it feels like a fact. This that might even be considered an oddity of the English language.
As to quod, you haven't given an example. Perhaps you were thinking of its use as a relative pronoun?
Templum aedificaverunt quod omnes finitimi inviderent.
"They built a temple (of a quality) such that all neighbours envied it."
Whenever relative pronouns are used to define something, such that you can translate them as "such that", the relative clause is felt to be consecutive, akin to ut "such that", whence the subjunctive.
Another possible translation is "they built a temple, in order that all neighbours should envy it". Then the use of relative + subjunctive isn't defining–consecutive, but final (indicating purpose).
Yet another construction is quod "because" with a subjunctive:
Nero servos misit ad domum Agrippinae, quod timeret ne mater vulnerata esset.
"Nero sent slaves to the house of his mother Agrippina, because he (claimed that he) was afraid she had been wounded."
The subjunctive (timeret) can be used with quod ("because") to express that it is not the author who professes this reason/cause, but rather someone else. The author does not commit himself to the truth of the quod clause. He may doubt or disavow Nero's motives for sending the slaves (is Nero intending to have her killed?). The author might simply not know whether that was the true reason. Had he considered it a fact that Nero sent the slaves because he was afraid for her, he would have used the indicative.