I can enlighten you as to the fact that at least 3 professional organists (who shall remain nameless) were given sight of this programme's script for checking technical facts. You'll find with most TV programmes that 'experts' are consulted as you suggest, but of course no mere mortal can claim to be omniscient and with the added dangers of electronic cutting-and-pasting and subbing-down, the odd 'rogue' addition or subtraction often works its way in and is missed by everyone at every stage.
Sometimes the presenter's availability means that a 'take' where he/she didn't quite stress the right emphasis ends up having to be used, and given the tight schedule and tiny budget, the producer has to judge whether the result is trivial or a serious misrepresentation. Sorry to sound like an anorak, but I have worked in TV and Radio production for years, and once something has been recorded in a particular acoustic, audio can't just be 'spliced in'.
Interesting that so few people seem to have 'got' the Gedeckt/Gedacht pun - I've made recordings of many organs over the years and I have heard this joke made by organists both in England and Germany (especially the latter where, given our love of the 'Wortspiel', there are linguistic reasons for believing that the spelling 'Gedackt/Gedacht' is deliberate).
This programme on the Organ was first suggested in 1999; and thereafter several times yearly until it was finally commissioned. Despite its early transmission time (resulting in low audience figures) I am happy to report that it seems to have been greatly appreciated by BBC1s non-organist audience.