We took our son down to the embassy today to register him. Our appointment was for 10am, but between a late-running train and having to drop our electronics off at the local chemist, we didn't get in until 10:20 or so. Nobody seemed to mind, and getting through security with a changing bag and stroller/pushchair was no problem.
After security we got to the first counter where an embassy worker checked through our documents to make sure we had everything. It was at this point that I realized I hadn't brought our marriage certificate. The woman said we could go ahead and they'd probably mark our application as pending until we sent in the marriage certificate.
We got and paid for our courier envelope, and then got assigned a number and proceeded up to the waiting room. They called our number within a couple of minutes, and I gave all our documents to the worker at the window. I had filled out a part of the form that I didn't need to, so she gave me another copy of the page and had me redo it.
I was called back about 20 minutes later to explain why our marriage certificate wasn't included, and got the same "we'll probably make it a pending application" answer.
After another 30 or so minutes we were called up again. This time we were asked a bunch of questions about where we got married, how many people came, and what interesting things happened during the planning and the wedding itself. After this, the interviewer said she was satisfied we had a genuine marriage, and our application was approved, and we'd get the baby's passport and SSN from the courier in a few weeks.
All in all we were there for a little over an hour, and despite not having all the required documentation, we were approved anyway! Yay, US Embassy!