I have a US passport that lists my current state as my birth state (Virginia instead of California). I am travelling to England next week and do not have time to get it corrected. Will this be an issue?
Nobody in England will care where exactly you were born - you are a US citizen, that is the only relevant data for them. If you don't bring it up yourself, they have no way to even realize it.
You should however care to get it corrected soon, otherwise it might hunt you in the future in the US.