I am applying for a US passport as a natural-born US citizen. On my passport application, I listed the city and state I was born in. I was just looking at my birth certificate however, and it lists the county I was born in, rather than the city. Will this cause the Post Office or the State Department to deny my passport?
The passport application asks for the city, you put the city. It does not matter that the city is not specifically listed on your birth certificate but rather the county. The US Dept of State will not expect you to change the laws around birth certificates for your state just to get them to add the city to your birth certificate. Do not worry about it, you provided what they asked.