As someone who has flown many post-major servicing maintenance test flights on the VC10K, the thing which immediately struck me when reading the CVR transcript was the woeful attitude towards flight testing exhibited by the crew.
I see no indication of a pre-planned flight, no indication of a test card with mandatory height/speed/configuration test points, just an "OK, I think we'll do this next" attitude - and rather weak knowledge of the characteristics of the flight laws.
Post-maintenance testing requires a highly disciplined approach, an experienced test team and a thoroughly pre-briefed flight with prepared test cards. It isn't the same as raw 'test flying' and doesn't necessarily need a fully qualified TP, but it DOES require a selected and well-trained crew with better than normal aircraft system knowledge.
Unexpected things may well happen during post-maintenance test flying - I once last half of the entire electrical system and all attitude instruments until we managed to relight the associated engine and get its alternator on line. (Good thing we didn't drop the ELRAT; on the next test flight its alternator control unit caught fire causing smoke on the flight deck during the approach...
)