Aside from the sense of the narrative and the language regarding its extent (fairly significant considerations), and the marks of the flood over the planet, there are theological issues that turn on the extent.
The flood is a counterpoint to the creation; as the creation is a total production that is 'very good' the flood is an 'unproduction' given the 'very bad' that God sees in rampant sin.
A local flood would make this literary and theological point nonsensical: the very good has become the very bad that God seeks to 'un create' at a significant level: to uncreate mankind.
This also builds the pattern of salvation: that God will and does rescue in the midst of that which rejects him, his love, and his nature (to love): despite the reaction to his love being rejected and denied (by sinful behaviour) in wanting to destroy: showing us the depth of betrayal, he acts to save, and does so. Salvation is a 'totalising' move by God and is rendered pointless by a local flood.
