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The adverb "quite" has the following meanings according to the Merriam-Webster dictionary:

1: wholly, completely ("not quite
finished")

2: to an extreme : positively "quite
sure" —often used as an intensifier
with a "quite a swell guy" "quite a
beauty"

3: to a considerable extent : rather
("quite near")

My understanding is that #1 and #2 conflict with #3. For example, when you say "She's quite right", do you mean "She's completely right" or "To a considerable extent, she's right"? Notice that in the latter case you're not saying that she is completely right.

Another example is "I'm quite sure". Does it necessarily mean "I'm completely sure"?

Does the word really have conflicting meanings that can possibly cause ambiguity? Or am I missing something?

No, you're not missing anything - the word has ambiguous definitions.

When it's used with an absolute, like correct or complete, people generally mean #1 or #2. When someone says, "Quite nice, I'm sure," watch out.

"Quite!" as in, "Hear, hear!" or "indubitably!"

There is a distinct bias toward the opinion of the speaker with this word usage. It implies "completely" while simultaneously allowing for factual refutation:

"He was quite close to falling off the cliff!"

"On the contrary, he was several feet away from the cliff. He was quite safe from a fall."

"Being so near to the cliff is quite the same as having nearly fallen!"

"Quite so, and yet he was never at risk for having fallen."

In this exchange, the opinion of the first speaker is that the object person was very close.
The respondent begs to differ, asserting the object person was very safe.
The initial speaker counters with a circular reply.
The respondent refutes the reply by agreement.

The term "quite" is not an absolute, it is a conditional that implies conditions nearly identical to certainty, yet lacking certainty.

Many languages have words with more than one meaning and English is no exception. That is without considering tone. English is made more difficult by the geographical spread of the user base leading to words having different meanings in different cultures or locales, including between England and Scotland.

Considered from a standard English English perspective, your examples 1 and 3 give the two meanings normally attributed to the word "quite", however in example 2 you mix both, as "quite sure" would come under example 1, while the others would come under example 3.

There is also a dialectal difference. American speakers tend to use it in the first two senses and British and Australian speakers in the third sense. But for both groups, the senses are all available, and stress and intonation might also have a role in deciding which sense is relevant.

I speak a British-style English. If I say that something is 'quite good', my normal meaning of that phrase is 'rather good' or 'somewhat good' (sense 3). However, if I put the stress on quite, it means 'completely good' (sense 1).

If an adjective describing an extreme quality is used with quite, then it can only be used in the first sense: therefore, 'quite exquisite' means 'absolutely exquisite'; 'quite revolting' would usually mean 'absolutely revolting'.

I've just seen this a post.
I'm involved in writing English courses for speakers of other languages. Our explanation of the different meanings of the adverb "quite" is as follows:
- when followed by a non-gradable adjective (one that cannot be preceded by "very"), quite means "absolutely" (e.g. quite right, quite mad, quite perfect, etc.
- when followed by a gradable adjective, quite means fairly (e.g. quite good, quite warm, etc.
I'm a British English speaker, so I can't vouch for the use in American English.

its not that ambiguous, as all its meanings refer to bringing something close to the subject (almost: #1) or used to refer closeness to the object (#2 and #3).

Note that you can substitute other words and the perceived ambiguity remains.

Not totally finished.

Totally finished

Totally near.

The word very essentially behaves this way, as well as really:

Not very good (Not necessarily bad, but falls short of being good.)

Very good (Does not fall short of being good. Better than good.)

Very near (Not there, but not far.)

The issue translates into other languages. E.g. Slovak's celkom (celok == the whole part, celkom is a case of this word which literally means by means of the whole part, or on the whole).

celkom hotové (quite ready)

nie celkom hotové (not quite ready)

celkom blízko (quite close)

Since there is evidence that the issue affects more than one word, and can cross languages, that suggests it might be a semantic issue, related to how words which intensify relate to other semantic concepts like completion, noncompletion or proximity.