nornen:
Case marking seems to have several exceptions in Eo. For instance adverbs mark accusative of direction (hejme -> hejmen), but they don't mark accusative when they are a direct object:

Zamenhof:Vi vidis multe, sed vi ne konservis

Perhaps a clearer term here is generalizability (is that a word? ĝeneraligebleco). A certain part of speech uses the ending -n a certain way, and you can safely generalize its use to all members of that part of speech (although not accusative adverbs will make sense, one at least knows they are in principle creatable).

Likewise, for nouns and pronouns, we seem to have a very consistent pattern for forming the accusative. It is even more consistent than plurals when we get to the somewhat aberrant pronouns (mi -> min, but mi -> ni, not *mij). Neniu - neniun. Ĉaro - ĉaron, etc. Suddenly we are told that one [pro]noun, unu, has no overt accusative singular. So: Exception to a rule!

EDIT: I'm also not sure I agree that "multe" in your quote is actually a direct object. Can adverbs even be direct objects?.. Here it seems to simply describe in what manner vi vidis - i.e., you saw much-ly, you saw in a bountiful manner ... (Doesn't quite work in English)

Tempodivalse:EDIT: I'm also not sure I agree that "multe" in your quote is actually a direct object. Can adverbs even be direct objects?.. Here it seems to simply describe in what manner vi vidis - i.e., you saw much-ly, you saw in a bountiful manner ... (Doesn't quite work in English)

Compare the following sentences which are semantically identical (unless one wants to interpret some "nuanco" into them):
Mi vidas multajn homojn.
Mi vidas multe da homoj.

Subject - verb - object in both cases.

There are other words that don't take -n:
Mi vidis ambaux.
Mi prenis tiom, kiom mi volis.

This has puzzled others.

here...

Nornen:There are other words that don't take -n:
Mi vidis ambaux.
Mi prenis tiom, kiom mi volis.

Absolutely.

I return Tempo, to my original point about word formation in Esperanto.

With the solstarivaj radikoj (the words that are already words without a grammatical ending), you may add a grammatical ending if there is a point to that (creates additional meaning), and if there isn't then don't add a grammatical ending.

So the rarity or complete absence of 'unun' should not be considered an exception.

I may need to add an 'n', because Ĉu mi vi amas leaves me not knowing whether the meaning is Ĉu mi vin amas or Ĉu min vi amas, but I can perfectly well understand Mi amas unu fraŭlinon and distinguish it from Unu fraŭlino amas min, just as I can perfectly well understand Mi amas ambaŭ and Ambaŭ min amas.

If you can think of a sentence where you need to add an 'n' to unu, to make the meaning clear, then you may well add it. But the point about such stand alone roots is that they don't have to have grammatical endings.

And even in the case of ne-solstarivaj radikoj (grammatical ending compulsory) not all grammatical endings are added. Whilst there is a use for bicikli, the verb arbi is not used - which hardly justifies calling arb(o) exceptional.