I think that the general meaning of "uncleanness" in Deuteronomy 24:1 is reasonably clear - it's about something to do with the genitals. It's sexual in some way. But that's not exactly specific.
The LXX confirms this.
The definition of
ἀσχημοσύνη is "an indecency; by implication, the pudenda:—shame, that which is unseemly." - essentially the same definition as the Hebrew.
Nevertheless, because you can debate the meaning of an individual word in a brief passage:
So Jesus explained it again clearly, using a different word with the same general meaning:
He defined the just reason for divorce clearly as being "sexual immorality" - "porneia". If we view Jesus in this case as a preacher explaining what the scriptures mean in practice (as any good preacher should), it is all completely clear and there is no disagreement between him and Moses. To explain what something means you say the same thing using different words - which is what Jesus did.
He clarified that Moses did not use that word in a figurative sense to mean "anything the husband doesn't like", but was using it in a literal sense to mean actual sexual immorality. Now there is no doubt over what the justifiable reason for divorce is, because we have the same thing explained multiple times in different ways, each of which adds to our understanding.
A woman who commits sexual immorality can be divorced for cause.