1) Chazal (at least, those in Babylonia) were of the view that the world is basically flat, with a slight rise to Israel and Jerusalem at the center. (See my monograph The Sun's Path At Night for sources.)
2) The Rishonim, for the most part, knew that the world is a sphere. However, they believed that the lower half was entirely uninhabited. To quote a comment by R. David Ohsie: "The Rishonim, like others, made the assumption that the inhabited part of the world spanned approximately 12 timezones. Naturally, the eastern edge had the earliest times and the western edge had the latest times. There was no need for a "dateline" per se because civilization did not wrap around the globe. The question of where exactly the day turns would be completely theoretical and probably was not considered important; it certainly had no meaning in halacha."
3) Most recent halachic authorities to weigh in on the topic of the dateline probably did not realize/ accept the previous two points. (A notable exception would be R. Menachem Kasher.)
4) To what extent can a halachic dateline be implemented? Here is another fascinating comment from R. David Ohsie:
I want to point out one other huge problem with any "degree" based dateline, especially ones that are close to Asia. We have a general principle that the Torah can be applied with the technology available in ancient times. Anything that requires modern technology, such as a microscope, is not considered imperative. Now in ancient times, there was no way to measure latitude accurately, nor generally to map the extent of landmasses. So to say that the halacha requires you to know that Indonesia is less than 90* from Jerusalem while Japan is greater than 90* or that the western tip of Australia is less than 90* from Jerusalem while you are sitting in the eastern side would be beyond what the halacha required. So more than the fact that the Torah never says where the dateline is, it could not have required a dateline, since that would require the knowledge of modern technology to implement.
5) There is a basic distinction between the mystical and rationalist schools of thought regarding concepts such as sanctity, whether of items, rituals or dates. According to the mystical school of thought, the sanctity of these things exists as an actual metaphysical entity. According to the rationalist school of thought, on the other hand, the sanctity of these items is a state of designation. For extensive and excellent discussion, see Menachem Kellner, Maimonides' Confrontation With Mysticism (which is the most fundamentally important book for anyone interested in rationalist Judaism).