Boeing and the FAA proceed on these things as a partnership. Boeing has their name on the line, and they have way more engineers and other technical specialists than the FAA. In the past, Boeing has essentially written the specs that must be adhered to by all equipment producers, and, once the FAA approves those specs and procedures, ensures that they are followed. This book gets into how this worked with the 747:

https://www.amazon.com/747-Creating-Worlds-Adventures-Aviati...

Would highly recommend this book by Joe Sutter the engineering leader for the 747 program: http://www.amazon.com/747-Creating-Worlds-Adventures-Aviatio...

IIRC, they had a lot of problems with engine failures, as the 747 really pushed engine technology and size at the time. Joe Sutter's book [1] is an interesting look at the history of the 747 design (he was the lead designer).

There was also an issue with the wing resonating, which they fixed by putting trim weights in the wing of the 747-100 made of depleted uranium.

[1] http://www.amazon.com/747-Creating-Worlds-Adventures-Aviatio...