I did not see the programme, so therefore cannot comment on it directly, but having read most of this thread there are a couple of things that I would like to add.
In circumstances such as this, it is often all too easy and convenient to place at least some, if not all, of the blame on to the flightcrew. These guys are dead and therefore cannot defend themselves, and can be libled and slandered with no recourse.
Okay, so what if the first officers medical certificate was lapsed, illegal yes, unprofessional yes, but did it contribute to the events in any way? No. Also, unless every crewmember, passenger, bag, cargo panier and galley cart is individually weighed then there will be an error in actual TOW. Using average assumed weights will yield an approximate TOW only. There will also be errors due to inaccuracies in the fuel quantity indicating system. I'd be very surprised if there was not at least a 1% error between estimated and actual TOW's on most big jet flights. Perf charts are factored to take account of all this, and again, 1.5 tonnes overweight did not contribute to what happened, so why bring it up??? We already know the chain of events; FOD, high energy tyre failure, fuel tank puncture etc. etc.
Lastly, this talk of missing shims. JH is a nice guy (met him a couple of times), and no doubt a skilled and experienced aviator, but it seems he just said too much here. In my experience (as a flight engineer and ex spanner basher!) most pilots are just not qualified to make such comments, their only technical knowledge coming from ATPL textbooks. Most would not know what a shim was, let alone what it was for!