Let It Be

The last concert The Beatles ever held, right here.

"I'd like to say 'Thank you' on behalf of the group and ourselves, and I hope we passed the audition!"

—John Lennon

The last film The Beatles made before their break-up. It is a Documentary/Rockumentary that covers what was supposed to be the making of an album and the concert that followed. This didn't work out well because different Beatles had different ideas about what should be done with the project and how it should be done. The personal relationships between the members of the band were also decaying quite rapidly at the time, which the movie quite bluntly reveals; several scenes involve the members of the band arguing and sniping pettily with each other. The concert ended up being held on the rooftop of the building of Apple Corps.

This film was released about a year later than planned; it took that long for there to be any consensus about what the accompanying album would be like. Unfortunately, it was an incomplete consensus; while John Lennon and George Harrison were happy with it, Paul McCartney wasn't even aware of the finishing touches until they were a fait accompli. This led to a chain of events that led to the film being released in May 1970--and after Paul had issued a press release saying he was leaving the band indefinitely. Instant Harsher in Hindsight, since this film already depicted stressful relations between the Beatles.

Tropes used in Let It Be include:

Breakaway Pop Hit: the entire Let It Be album, and especially "Let It Be" and "Long and Winding Road."
Creative Differences: And how. In particular, one famous scene features Paul and George sniping passive aggressively at each other over a chord.
Deleted Scene: Lindsay-Hogg cut a LOT out of his movie. There is no trace of the violent argument between John and George that (legend has it) came to blows, no mention of George quitting the band in the middle of the sessions, and no hint that the sessions were suspended for nine days while the Beatles figured out what to do next. Additionally, Billy Preston materializes at Apple with no explanation. (George brought his friend in to support the Beatles' live ensemble with keyboards, and to help calm down a fractious group.)
Documentary
Evolving Music: We see the band running through a hard rock version of "Two of Us" during the Twickenham sessions. When they play the finished version in the studio, it is a mellow acoustic pop song.
Finagle's Law: there were many disasters in the making of this film--many of them filmed.
Ice Cream Koan
It Got Worse
Keep Circulating the Tapes: This film was last available on the free market (on VHS and laserdisc) in 1991. It has been pulled until it can be remade into something that the current heads of Apple (Paul, Ringo, Yoko Ono, and Olivia Harrison) can find acceptable. Even after the release of Let It Be...Naked (a remix of the Let It Be album), it hasn't been a high priority. Netflix had it for some time, but it vanished again.
Missing Episode
Performance Video: Most of the movie, with the first portion being The Beatles rehearsing their new material and the latter portion being them playing the finished songs live. A careful viewer will notice that the finished products are mostly McCartney songs. George could not get the others to give his material equal attention, even while he was bringing gems like "All Things Must Pass" into the studio, and Lennon was at an all-time creative ebb.
Real Life Writes the Plot: whatever had been originally intended to be filmed, it probably wasn't what got filmed.
Rooftop Concert: Trope Codifier. What most people don't remember is that the Apple rooftop performance only came after the band tried and failed to agree on anywhere else to play the planned live show--a North African ampitheatre, a cruise ship, the Royal Albert Hall, etc. After failing to come up with anything better they simply went to the top of their own building. And they still managed an iconic, much imitated rock music moment.
A Simple Plan: The Beatles had already tried to get out of their obligation for a fourth movie with Yellow Submarine. Failing that, this was probably seen as the next easiest thing to do.
Throw It In: Lots of Studio Chatter is thrown into the songs on the album, including the quote above, which closes the album in the same way it closes the film.
Troubled Production: It wound up being a documentary on one.
Wag the Director -- Paul attempts this, unsuccessfully.
Yoko Oh No: She's there watching the whole thing, but except for dancing with John, she doesn't really say or do much. The Beatles manage to create enough conflict by themselves.