I recently asked a question here about getting an official marriage license translation. It turned out that the issue was completely different, but I misunderstood what the immigration officer was asking some months ago.

My wife - also American - and I went to do our visa extension today in Hua Hin, and we got an officer who speaks good English. He would not accept our marriage certificate (a copy certified by the county's issuing authority, but not the original because that is kept in their official public records archive), because the copy's authenticity had not been verified by the US Embassy. They want us to get our statement of authenticity notarized by the Embassy, then they will process our extension.

We have a few weeks before our visas expire, so we don't anticipate any issue there. On the other hand, we do live about 250 km from Bangkok, so that part will be a bit of a pain.

Another interesting thing they required: they wanted me to draw a map to our house. I pulled up Google maps and showed them the exact location (I have it saved), but they insisted on a hand-drawn map.