Especially in places like Ancient Greece where oracles were kind of run like businesses, how would people rationalise a supposedly divine prediction that just wasn’t at all accurate? (I understand that predictions were usually pretty vague to avoid precisely this, but even then there must have been quite a few that just don’t work any way you look at it)
The situation pretty much never arose, because in real life oracles didn't make predictions. They gave instructions.
We've got two kinds of sources for oracles:
Literary sources like Herodotus.
Epigraphic sources (official inscriptions commemorating an event) and documentary sources in a legal context.
We also have two kinds of categories of oracles:
Oracles that foretell the future; obscure and/or ambiguous oracles; oracles in verse; oracles with metaphorical imagery, especially animal imagery; oracles with 'if'/'when' clauses.
Direct instructions; oracles that say yes or no, do this or do that, you're OK to build on this plot of land or it should stay sacred and unbuilt.
Two kinds of sources, two kinds of oracles ... and that's no coincidence.
In both cases, the second category is the kind that existed in real life and was given at institutions like Delphi. The first kind is basically mythological. It's fictional. And it has a separate origin, not directly related to real institutional oracles. (At least until the Roman era: at that time, life seems to have begun to imitate art, but our evidence is pretty unclear at that time.)
Now, it's true, Herodotus was writing about events only a few decades before his lifetime. But that didn't give him immunity to error on this point: he wasn't the one consulting the oracles. Someone who can report the story of Croesus' test of the oracles to see which one would know he was boiling tortoises, and take that story seriously, is someone who can't be relied on for precision about institutional oracles.
More importantly, we have a much better candidate for the origin of the mythological-style oracles that we see in Herodotus: a genre of poetry called 'oracle collectors'. The oracle collectors were themselves sometimes legendary and unreal. Some of the major names are Bacis, Musaeus, Onomacritus, and Abaris. Several sources quote bits of their oracles. And what we see in those quotations is an exact match for the 'mythological' style of oracle.
As a well known example, let's take the wooden wall oracle in Herodotus. This supposedly predicted that Athens would successfully defend itself against the Persian invasion by naval force. It's intrinsically unreal. It's an accurate prediction of the future, and we go into this kind of material with a presumption that accurate predictions of the future aren't real. That implies that the wooden wall oracle was composed after Salamis; that means it wasn't an oracle given to Themistocles; and that means it almost certainly didn't come from Delphi.
That gives us two alternatives: (1) The oracle actually comes from somewhere else -- one of the oracle collectors. (2) Delphi's oracle publication office wrote it after the battle of Salamis, and somehow got people to think it was older.
Option (2) is possible, but option (1) has the support of everything we know about oracle collectors as a literary genre. It's clear that option (1) is going to be the more impactful origin for 'mythological'-style oracles.
It's conceivable that pronouncements from major institutions were sometimes converted to the 'mythological' genre for public dissemination. It's also possible that the oracle collectors had some kind of interaction with the institutional oracles. We know that some oracles did have an oracle writing office, and it's possible that an office like that was an interface between the two genres. Maybe, for example, the oracle writing offices imitated the oracle collectors; or maybe the relationship was two-way. We don't know.
The key point is that of mythological-style vs. real oracles, predictions vs. instructions, and oracle-collectors vs. real-life institutions, we have every reason to think of these groups as lined up nearly perfectly. If you consulted an oracle in real life, it's the second kind you would receive.
Here's a piece I wrote a couple of years ago that gives some more context and reading. For further reading in print, I recommend: