The Idea in Brief
The term "וְכָל־הָאָרֶץ" appears to refer not only to the general area of Palestine and/or the Fertile Crescent, but beyond to the known world at the time.
The Masoretic Text provides valuable clues. First, the photographic facsimiles of the Aleppo Codex and the Leningrad Codex indicate that the phrase "וְכָל־הָאָרֶץ" occurs five times in the Masoretic Text. That is, each codex contains the margin note (Masorah parva) of five occurrences, as indicated by the Hebrew letter ה̇ with the dot on top.
When we look at the End Notes or Footnotes (Masorah magna) of the Masoretic Texts, however, we see an anomaly. The late Gérard Weil analyzed and compiled these notes for the editors of the Biblia Hebraica Stuttgartensia. The following is his own entry for these five passages. Please click on the image to enlarge.
Please note the bracket marks. That is, the Masorah magna reflects four verses instead of five. Weil had to supply the fifth verse, which is the verse in question (1 Ki 10:24). And so we have to ask the question: why would the Masoretes indicate that this phrase occurred five times in the Sacred Text (as noted by the Masorah parva margin notes at the respective five verses), but in the Masorah magna reflect only four verses? In other words, why would the Masoretes have omitted (1 Ki 10:24) from the Masorah magna? We should not ascribe this omission to human error because in the Masorah magna the Masoretes omitted the Hebrew letter ה̇ with the dot on top. Note that Weil had to supply the ה̇ with the dot on top in his note on the Masorah magna (image, above).
There appear to be two obvious reasons.
First, according to the footnotes of the Biblia Hebraica Stuttgartensia for this particular verse, the Septuagint (translation of the Hebrew Bible into Greek) and the Peshitta (translation of the Hebrew Bible into Syriac) translate the phrase in this verse not as "all the earth" but "all the kings of the earth," which would be consistent with the following verse.
2 Chr 9:23 (NASB)
23 And all the kings of the earth were seeking the presence of Solomon, to hear his wisdom which God had put in his heart.
However, if we assume the Masoretes made the deliberate decision to omit this verse from the Masorah magna, then there may be another reason. In the first four instances where this phrase occurs in the Hebrew Bible, the meaning of "וְכָל־הָאָרֶץ" appears to be Palestine and/or the Fertile Crescent. By not grouping 1 Ki 10:24 with these first four verses, the Masoretes avoided the inference that the phrase "וְכָל־הָאָרֶץ" referred just to Palestine and/or the Fertile Crescent. In other words, consistent with 2 Chr 9:23, the phrase "וְכָל־הָאָרֶץ" would include the scope outside and beyond Palestine and/or the Fertile Crescent.
The Masoretes knew their Hebrew Bible "forwards and backwards," and even made allowances for apparent scribal errors through their own system of the "Qere and Ketiv." However, in this instance of 1 Ki 10:24, they avoided any grouping in the Masorah magna that would have grouped the phrase "וְכָל־הָאָרֶץ" with the other four exact phrases and occurrences in the Hebrew Bible, which were limited in scope to Palestine and/or the Fertile Crescent. By this omission, the Masoretes leave us to infer that the phrase would be more consistent if viewed through the lens of 2 Chr 9:23, where the context appears to open the scope of Solomon's reputation beyond the limits of Palestine and/or the Fertile Crescent. For example, the Queen of Sheba (1 Ki 10:1), appears to have come from southwestern Arabia.