Esperanto as presented in the definitions occasionally combines in one word meanings that in English are quite distinct: lasta means both final and most recent, for example (according to the text vortaro). Preciza means both precise and accurate, not the same thing. Numero means both number and numeral, not the same thing.

Is this right? or does Esperanto have separate words for number (the value, the abstract idea) and numeral (the physical expression)? If a poster has a large "3" and a diminutive "8", the numeral "3" is the larger but the number 3 is the smaller.

I do realize that often words do indeed have different meanings, but the examples I cite seem to be blurring a distinction that English makes.

The same you can say about English.
For example, "blue" is in Russian two distinct colors "голубой" and "синий".

Or from other theme:

I moved to United States = Mi transloĝiĝis al Usono
I moved a closet = Mi movis ŝrankon

Mixing lasta and pasinta is also sloppiness in my records (I admit having done that myself). On the other hand my native language doesn't even distinguish between nombro, numero and cifero, so why would I care about the difference between a number and its glyph (IIUC your example).

Different languages use different ways to express the ideas. What I've stumbled on in many occasions is the perception of movement or lack thereof. I would prefer to say:
 

• I buy from a store : Mi aĉetas de vendejo.
  
• I read from a newspaper : Mi legas de sur gazeto.
  
• I go into that direction : Mi iras en tiun direkton.

but I know that I would get flagged by some.

Yes, there is a lot of sloppiness and many speakers/writers use expressions and constructs from their native language, most do that certainly inadvertently. Unless we are speaking of mathematics or sciences, which require precision, we are already imprecise in our native languages, but in many cases it doesn't matter as long as the message stays sufficiently clear.

This has nothing to do with sloppiness, but with the fact, that each language divides the "semantic space" (i.e. the space containing all ideas we want and can express with words) differently. Some are more precise in one spot and "sloppier" in another, while with other languages it is the other way round.
We must not say "language A is sloppier than language B, because two different words of B map to only one word in A", because we will always find examples where it is the other way round.

Sergej gave a very good example: English "blue" versus Russian "голубой" and "синий". The same is true for Spanish "celeste" and "azul".

Now English has two words "divide" and "share" which for English speakers denote something quite different. This doesn't stop other languages like German or Esperanto to just use a single word covering both meanings, "teilen" and "dividi" respectively.

Also English "to be" translates to Spanish as both "ser" and "estar" and these two denote quite different things. The distinction between "Es rojo (it is red)" and "Está rojo (it is red)" is simply lost in English.

In the case, that we find two (for us quite different) words in our language which translate to the same word in Esperanto, we should not try to coin new words to iron out this "sloppiness" or "lack of precision". I think, we should just accept that this single word works fine for both.

About "last" vs "latest". Fun fact: "last" is just a syncopated variant of "latest". And their meaning isn't that different at all. The latest record of a band is always also their last record until the moment they publish a new one.
The division between "last = final" and "latest = most recent" isn't even that strict in English. Surely, 2000 was the last (final) year of the XXth century, but I can also say (please do correct me if I am wrong) "Last summer I went to Europe" although I hope the summer of 2019 wasn't the final summer in human history, but only the most recent one (=latest).
Even Oxford Learner's Dictionary defines "last" as both "happening or coming after all other similar things or people" and "most recent".
Look on the bright side: In Esperanto you don't need to worry about whether to use "last" or "latest". "Lasta" will always do the trick.

All very good points. To take a canonical (and perhaps apocryphal) example, English has one word "snow" whereas Inuit languages reputedly have many, though English has workarounds for some (e.g., powder (referring to snow), slush (melting snow), wet snow, icy snow, etc.).

And I have to agree that "last summer" is a common phrase for "most recent" summer. Still, there seems to me to be a difference between (say) Bruce Springsteen's last album and the Beatles' last album. (However, the phrase "his last summer" has a note of finality about it.)

The number/numeral distinction leapt out at me because for a while I wrote elementary school textbooks, but of course one could use numero skribita for numeral. And the difference between precision and accuracy stuck with me from my undergraduate lab work.

I suppose it comes down to all languages being "sloppy" in not making distinctions that are unimportant to speakers of that language, and when the distinction becomes important, the language evolves by the creation of a new word or using an old word in a new sense.

Right now I'm trying to figure out the Esperanto equivalent of "skillet" — fritpanjo? [update: I just discover pato = frying pan. Mi ofte uzas giza pato.] And cutting board: tranĉtabulo? — UPDATE: Aha! I just found haktabulo. I didn't know "haki" before.

I'm making an Anki deck of words for the things I use around the apartment so I can talk to myself in Esperanto about what I'm doing....

A general dictionnary is not very good to translate words that have a more rigourous meaning in sciences than in current language.
The word "akurata" is available in Esperanto.
It is better to look in scientific textes how the words "precizeco", "akurateco", "preciza", "akurata" are used.

Nornen makes a good point. Different languages divide up the semantic space differently.

However Esperanto occupies a somewhat special position. It is a language which has no monolinguals. All speakers speak at least one other language, which is not true of the speakers of most other languages

It has a flexibility in vocab construction which is not equalled, and explicit principles in relation to the introduction of new roots.

(By the way, Leisure Guy, Esperanto has fairly rich range of options with regard to 'number' - nombro, cifero, numero, and numeralo.)

Anyway, back on topic, I would say that it works like this. If there is a large group of speakers of a particular mother tongue which makes a distinction that up to a certain point in time Esperanto hasn't distinguished with separate roots. they may be content with some compound word or other work around, or they may launch a root initiative. And if the latter catches on then it enters the language.

As far as I know, the Russian distinction between two types of blue has not resulted in a new root appearing in Esperanto. However if there had been a predominance of Russians speaking Esperanto, it might have done.

However, you could probably find a good few of examples of distinctions considered important by Esperantists of a certain mother tongue which have entered the language at a root level.

the Beatles' last concert. La finala koncerto?

Yes, that's better than la lasta koncerto, but since lasta means both last and latest, lasta could be used — still, I think la finala works better. And I like Metsis's pasinta instead of lasta when meaning "most recent," a usage reflected in English when one says "this past summer" rather than "last summer" (though I admit "last summer" is not ambiguous — it just distorts the meaning of last.

It's interesting that using the possessive seems to put a twist of finality on "last" — "Did you see Scorsese's last movie?" sure sounds like that's the last one. "His last book," as a phrase in isolation, suggests that we're talking about an author who lives no more, whereas "his latest book" clearly suggests that there may be more books to come.

Still, I think the point is well-taken that all languages include ambiguous words where, for whatever reason, the distinction the words obscure is unimportant to most speakers (though in a technical field, the distinction may be important, so that the language in those fields is more carefully wrought — cf. the distinction between "accurate" and "precise" in science (and probably in engineering as well). For most, the two words can be treated as synonyms since the distinction is not so important.

Aha! Esperanto does distinguish between "number" and "numeral":

nombro = number
numero = numeral

And actually Lernu's vortaro does make the distinction.

I was wrong.