Perhaps I should wait for you to release the paper, but there's one issue which I'd be interested to hear your views on which arises from an infinite Earth.
An infinite Earth requires infinite matter, which leads to a problem touched on in D W Scott's "Terra Firma 1901".
To quote the book:
...when there are countless millions of things, both celestial and terrestrial, all struggling at the same time to attract each other, such a law [gravity], from the inextricable confusion which it would necessarily create, would not only be an absurdity but an impossibility.
What I'm getting at is this. If gravity exists, and if the Earth is an infinite plane, the force of gravity must necessarily be infinite in a given direction. Though the force greatly diminishes with distance, the distance from one object to any other object will necessarily be finite - consequently some amount of gravity will still be exerted. This effect compounded to infinity would, if I'm not mistaken, render existence as we know it entirely impossible. An infinitely strong gravitational pull would instantaneously attract matter to its source, compacting the universe into nothingness. I appreciate that the Earth as a whole would have no centre of gravity, but any arbitrary article of matter would.
I'm interested to hear your take on this, but if you'd rather deal with it in what you're working on, I'll gladly wait.