"It looks scandalously risque now," Mr Fiddy says. "It's years ahead of its time in that way, as the word 'adultery' very rarely cropped up in a sitcom until much later on in the '60s.
"But in this one, Bob's been married for seven years and he's got the seven-year itch; the Marilyn Monroe film on that subject was in the news at the time.
"A model moves in next door and he watches her through binoculars when she's in the bath, and stuff like that. It's very non-PC."
The Flip Side, a BBC play from 1966 in which Monkhouse appears as a DJ with a late-night television show, will also be screened.
"The DJ plays music but also engages in right-wing political banter and, while he's playing the records, you realise his personal life is in tatters.
"It's a very good performance. It's not funny, although there are funny moments. It's very much a drama."
Monkhouse (right) played a DJ in My Pal Bob, screened at Sunday's event
The BFI also uncovered a wealth of written material in which Monkhouse "made copious notes" about his vast collection of recordings.
"He had satellite dishes and probably half a dozen recorders whirring away in all parts of the house, some of them on satellite stations that he'd picked up from a moveable dish in his garden," says Mr Fiddy.
"As a snapshot of television at that time, all of this can be incredibly valuable.
"Any collection like this, by accident, also has continuity on. Tapes have weather forecasts, continuity girls, trailers for things. Those things are largely missing before about 1980 and that can be quite interesting."
As well as the Monkhouse material, those attending Sunday's show will see long-lost trailers for BBC programmes from the 1960s plus rare Top of the Pops performances which have been unearthed this year.
The restoration technique turned the black-and-white recording into colour
There will also be an explanation of a new preservation technique which can turn certain black-and-white footage into colour.
Black-and-white back-up copies of many BBC programmes were made in the '60s and '70s so the colour master tapes could be erased and reused.
But patterns of colour - known as "chroma dots" - were accidentally left on some of these back-up recordings.
BBC archivist James Insell, who will address the BFI event, began a restoration project after being intrigued by patches of red dots on a black-and-white Doctor Who film.
BBC Radio WM's Ed Doolan explains how he helped to restore Dad's Army episodes
"In a way this is an accidental preservation of the colour information because the people who were making these recordings in the '70s were supposed to be filtering this out," he says.
"Luckily they didn't always do this and it's given us the potential to restore programmes where we thought the colour versions had been lost years ago."
The technique has been used for the first time on an episode of Dad's Army - Room at the Bottom - which is being screened as part of a Dad's Army evening on BBC Two on Saturday.
This edition has not been seen in colour for nearly 40 years.
As for Monkhouse's material, the BFI and television-archiving association Kaleidoscope continue to sift through thousands of tapes and could yet discover some hidden gems.
"I hope there may be a couple of 'lost' Sunday Nights at the London Palladium in there," says Mr Fiddy.
"In an ideal world there'd be a comedy museum in Britain in which you could have the 'Bob Monkhouse room' and just go and wander through his stuff.
"But until someone opens that, what we're left with is the legacy of a guy who was fanatically interested in this field, and sadly nowhere to deposit it."
Missing Believed Wiped is held on Sunday 14 December at the BFI Southbank cinema in London.
Dad's Army Night is broadcast on Saturday 13 December on BBC Two.
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