There are hints in cosmological observations that the speed of light may not be constant over sufficiently long timescales, and that the gravitational constant may vary over sufficiently long distances. (NB, both are speculative!)
What would it even mean for the speed of light to not be constant, other than we're using the wrong system of coordinates?
New Salt Compounds Challenge the Foundation of Chemistry
The title is overblown (it depends on what you think the foundation is), but get a load of this:
And here's the philosophical bit:
The obvious example of local truth is relativistic effects being pretty much invisible over the durations and distances that are normal for people, but there's also that the surface of the earth is near enough to flat for many human purposes.
Any suggestions for other truths which could turn out to be local?