I saw the programme too and was very impressed with its accuracy. From the usual sensationalist re-creations that American tv comes up with, this programme (and the others in the series ) are very well produced and a refreshing change. They even had the a/c registration correct (Romeo Tango) on the computer graphic simulations. The captain however, was depicted on the top of the a/c fully clothed. In fact he was stark bollock naked but I guess you can't show that on US Puritan tv in light of Janet Jackson's recent "wardrobe malfunction".
The engineer was not promoted to management as he already was a manager. He was de-moted to become a regular engineer.
I believe the pilots lobbied for him to be kept on with BA as they knew him to be an extremely experienced, conscientious and hard working person and was working on his own due to economic restrictions at BHX. I was aircrew at BHX for fifteen years and knew all the participants well. The wrong bolts had been fitted 4 years earlier by British Caledonian and BA inherited the a/c from them. B Cal had fitted bolts of the correct diameter but slightly shorter than specified.