Something about Nog's literacy history brings up a ton of weird questions in-universe.
- How are the Ferengi able to be a functional space-faring species and business empire without at least a little emphasis on literacy?
Even for as class-based a society as the Ferengi, lower level workers have to have at least a little literacy to read instrument panels, repair ships, make sure they're carrying the right package, etcetera.
I think a key example here is Rom, who starts out a relatively typical exploited Ferengi - how would he read manuals to repair a holosuite without literacy.
I see two explanations. One, perhaps by "reading", they're referring to reading of a lengua franca like Federation standard - Nog has learned and is capable of reading the Ferengi language, but not another. When dealing with other languages, the general expectation is either a universal translator is used or they pick it up as they go.
Alternatively, it could be that it is expected in Ferengi culture that reading is just something you pick up on the job rather than in a concerted educational effort.
- How did Nog manage to "catch up" fast enough to attain the educational level needed for a Starfleet officer?
Of course, it is said and implied that after the school closes, Keiko teaches Jake and Nog one-on-one. Some education definitely happened off-screen.
Still, Starfleet seems to have educational requirements. In LD:"Something Borrowed, Something Green", Tendi mentions how she wouldn't have gotten into the Academy without having gone to high school, suggesting Nog needs the equivalent of a high school education to train to be a Starfleet officer.
It sounds a little ridiculous to go from being unable to read to a full high school education in less than three years, though that could be a bigger stretch than I'm making it out to be.
I'd say the simplest explanation is probably that again, Nog was more educated than we might interpreting being "unable to read" to mean.
It might be possible Ferengi also have higher-than-human-average neuroplasticity and simply adapt easier - this might even aid in the on the job theory.
So what are your ten cents? Also, it's been a while - glad to be back on Daystrom.
This one is a bit of a copout, because Kim's official role as the ship's operations officer would absolutely have been appropriate for a higher ranking officer. It's the same job Data held as a Lieutenant Commander on the Enterprise; if anything, the strange bit is that it was given to a green ensign in the first place.
Ultimately, the real explanation is a much sillier bit of bad writing. According to Garret Wang, quoted here:
Why it was important that "somebody’s gotta be the ensign" is a mystery to me.