This is from Richie Unterberger's The Unreleased Beatles:
'As part of this documentary (which covered all types of British music), the Beatles were showing working on "Hey Jude" in the studio. Refreshingly, it wasn't just silent footage shown to a mimed finished record or some such thing. These were actual scenes, with actual sound, of them polishing a classic-in-progress, with actual unreleased music (though only heard in fits and starts) on the soundtrack. Paul's characteristic ebullience here is to be expected, but it's also interesting to note John's all-out enthusiasm; he might have been critical, sometimes nastily so, of some of Paul's songs after the Beatles broke up, but he always had high praise for "Hey Jude". The vocals are obviously a little too self-consciously, humorously exaggerated in this footage for a finished take, and it would actually take a couple more days of recording before the group had the finished track. "I keep getting me trousers caught on the pedal," complains Ringo mildly at the end of one version. "Take 'em off!" quips John.
There's an indication all might not have been happy behind the scenes, however, as George Harrison is not participating in the recordings at this stage, instead sitting in the control room with George Martin and engineer Ken Scott. Paul, as is now famous among Beatle scholars, had rejected George's idea for using responsive guitar phrases in the song, and at least at this stage his role in the recordings looks nearly nonexistent. There must be more footage that wasn't used, incidentally, as a few out-takes showed up (though without sound) in Anthology.
[...] Take 2 of "Hey Jude" on July 29 had an unrelated music-hallish intro and, for whatever reason, McCartney takes the same path here, vamping on a 15 second nightclubish impro that bootleggers usually titled "Las Vegas Tune" after the most prominent phrase in the lyrics. Following that is nearly a minute of noodling around on a recognizable standard, "St Louis Blues". "Hey Jude" isn't a song that comes to mind as an all-around-entertainer vehicle, but it seemed to spark, perhaps subconsciously, some of Paul's leanings in that direction, if only as a way to keep the atmosphere light between takes.
As if this wasn't enough, the Beatles were also filmed on this day for the documentary movie Music!, performing parts of some of the "Hey Jude" takes described above. This clip includes brief sections of other takes that seem unfinished enough to suggest they were done earlier in the session. There aren't any relevations to be heard, though Paul throws in a reference to Little Richard's "Tutti Frutti" at one point, and John a more off-the-wall enunciation of the "Beep beep yeah!" exclamation from "Drive My Car". And there's yet another tossed-off "St. Louis Blues", this one lasting just 15 seconds. That clip also shows how poor George Harrison didn't play at all on these sessions, instead sitting in the control room.
So, I guess they did two version of St Louis Blues, one being on film and a slightly longer version on Hey Jude outtakes. I couldn't find further information on more footage.