What's the approximate date and content of these three editions? There are two from '66 including the last show and the '63 edition that Andrew referred to which officially exist. Presumably it's these you are thinking of?
I reckon shows were recycled soon after transmission generally. There was no retrospective clips shown on Goodbye Lucky Stars as might have been expected.
I've found no conclusive proof that any material was repeated on later editions, as happened on Top of the Pops. Each show was treated as an ephemeral event.
The Merseyside edition has time clocks and you can hear the crowd being whipped into a frenzy by the director/producer inbetween the parts.
Here's a summary of what is out there.
Saturday 21st December 1963 5:50 - 6:35 pm. Episode still exists.
Host Brian Matthew
The Beatles: All My Loving, Twist And Shout, She Loves You, I Want To Hold Your Hand,
Gerry & The Pacemakers - You'll Never Walk Alone, I Like It
Billy J Kramer & The Dakotas - I'll Keep You Satisfied
The Searchers - Sugar and Spice
Cilla Black - Love Of The Loved
The Breakaways - That Boy Of Mine
Tommy Quickly – Kiss Me Now,
Janice Nicholls,
Bill Butler
Guest DJ Bob Wooler of The Cavern
Saturday 14th May 1966 Episode still exists.
Host: Jim Dale
The Rolling Stones: Lady Jane, Paint It Black,
Tom Jones: Responsible, Once There Was A Time,
The Koobas: You’d Better Make Up Your Mind,
Deano: Starlight,
The Morgan-James Duo: Put Your Tears Away,
The Kentuckians: She Thinks I Still Care,
Lorne Lesley: Somebody,
Ronnie Carroll: Wait For Me,
The Londonaires: Dearest Emma
Saturday 25th June 1966
ABC Goodbye Lucky Stars 5:50 - 6:35 pm. Still exists.
The Beatles: Paperback Writer, Rain promo clips
Roy C: Jumping Pneumonia
Ray Ellington and Cleo Laine: We Should Have
Ivy League: Willow Tree
Peter & Gordon: To Show I Love Her
Gene Pitney: Nobody Needs Your Love More Than I Do
Helen Shapiro: Shop Around
Miss Ruby Miller: Stop and Think
Herman’s Hermits: This Door Swings Both Ways
On the 20th of October 1963 the Fab Four returned to the Alpha Television Studios in Birmingham and mimed to three songs: All My Loving, Money (That's What I Want) and She Loves You.
The show was transmitted on the 26th October 1963.
The Money footage exists in good condition but it would appear that is the only song of the Beatles’ set to survive.
The Beatles mimed to four numbers on the 14th of November 64 and these were transmitted on the 21st of November.
The songs in question were I Feel Fine, She's A Woman, I'm A Loser and Rock And Roll Music.
All these songs exist as the Beatles appearance was taped in advance. It appears the footage was mistaken for newsreel and copies have been circulating for some time.
John mimes acoustic guitar and the harmonica for I'm A Loser.
The boys also indulged in some tomfoolery with the host Brian Matthew.
On the Beatles Anthology there is an extremely short clip of Brian Matthew.
A vtr insert of Gene Pitney exists as well. It’s been shown at least twice at Kal events. Gene does a Town Without Pity. This clip was shown in the B.B.C’s Rock and Roll Years for 62.
An episode of the Australian version of this UK pop music program which originally ran in the UK from 1961 to 1966 but only in Australia from 1964-65. Each Australian episode was a combination of clips from the UK original series and one local Australian artist, with the original UK host (Brian Matthew) replaced by an Australian one (John Bailey). This episode features The Dave Clark Five, The Merseybeats, The Redcaps, Doug Sheldon, Kathy Kirby and Australian guests, The Cicadas.
Australia seems a good bet for sources of surviving material.