The Dirty Mac Sessions

On December 10 1968, a link before the performance of the "Dirty Mac" band (with John Lennon on vocal/guitar, Eric Clapton on guitar, Keith Richards on bass and Mitch Mitchell on drums) was recorded. The link to the performance includes John sitting on a high bench with Mick Jagger and both introducing the "Dirty Mac" and the song "Yer Blues" (from the current LP "The White Album" as it was known). Both have a deadpan mocking voice calling each other "Winston" and "Michael".
The performance itself was recorded specially for the Rolling Stones' "Rock And Roll Circus" television special. The band was warming up on the afternoon of December 11 1968 when a blues jam was captured on tape. The blues jam can be found on the vinyl LP "The Lost Lennon Tapes Volume Eight" in mono.
As far as the song "Yer Blues" is concerned, there are two takes available from the camera tapes (nagra tapes) and one take available from the four-track audio tape. Take one from the camera tapes can be found on the vinyl bootleg LP "The Lost Lennon Tapes Volume Thirteen". Take two from the camera tapes can be found on the vinyl bootleg LP "The Lost Lennon Tapes Volume Eighteen".
If you are looking for the stereo version of take three of "Yer Blues" from the four-track tape you can find it on an old bootleg LP "Not for Sale".
There is an addition to "Yer Blues" when Yoko steps up to the mic with the encouragement from John and adds her vocals to a jam that the band are performing. This has been released under two names: "Her Blues" or "Whole Lotta Yoko". This masterpiece can be found on the bootleg LP "The Lost Lennon Tapes Volume Eight" as well.
Finally, both "Yer Blues" and "Whole Lotta Yoko" along with the introduction/link were released commercially in 1996 on the video tape/CD "Rock And Roll Circus".

December 1968 Lennon Demos

While Paul was working on the "Postcard" LP by Mary Hopkin for Apple Records, John Lennon was busy during the month of December 1968 working on some new songs
Most of the performances were conducted at his home (still) in Kenwood. The Beatles had agreed to meet in the New Year and start rehearsing for some kind of television special so some new songs might be in order.
We hear two versions of "Oh, My Love"; these are very John/Yoko centric and would evolve to the same title with changes for the eventual 1971 Lennon solo LP "Imagine".
We also get to hear the song "A Case Of The Blues" which is demoed during the month and you can hear some snippets of this tune during the "Get Back" rehearsals the following month but it was never properly recorded or released as a Beatles tune.
There is a demo of "Everyone Had a Hard Year". This riff and repetition would be added to Paul's number "I've Got A Feeling" as the Beatles would meet in a few weeks in January 1969 at Twickenham studio to start rehearsals for the television special.
Finally, two nice takes of "Don't Let Me Down" (very unfinished) have surfaced from these demos.
The tunes can be found on various "Lost Lennon Tapes" LP bootlegs. All of them can be heard on the bootleg CD "The 1968 Demos" and the "Oh My Love" outtakes can also be heard on the bootleg CD "Imagine...All the Outtakes".

The "Post Card" Sessions

At the end of the year 1968 during the months of November and December, Paul McCartney was busy at Trident Studios/ EMI Studios (mainly Trident) completing an LP with Apple artist Mary Hopkin. He is listed as the producer.
Paul also plays on the LP (of course) with the following instruments: Tambourine on "The Honeymoon Song" which was also performed by The Beatles on the BBC; "Happiness Runs" written by Donovan and featuring Mary Hopkin on the acoustic and Paul on bass; both Paul and Donovan play their acoustic guitars for the songs "Voyage of the Moon" and "Lord of the Reedy River". Another track, "The Puppy Song" written by Harry Nilsson has Paul playing piano.
"Love Is the Sweetest Thing" features Paul on the acoustic guitar alongside the band. Paul also plays acoustic on "Lullaby of the Leaves". Finally, Paul plays acoustic guitar, bass and drums on "Prince En Avignon".
All of these tunes can be found on the Apple LP/CD "Postcard" by Mary Hopkin.