Paul McCartney wrote "When I'm Sixty-Four" as a lighthearted song about a man who wonders if a woman will stay with him when he grows old. When Paul McCartney turned 64 in real life, his then-wife Heather Mills separated from him and they later divorced.
It had already taken on a somber note well before that, after the woman he originally wrote it for (Linda Eastman, his first wife) died.
On a slightly more humorous note, over the course of his 64th year of life, Paul had that song played and sung to him so many times he jokingly said he regretted ever writing it.
"Fixing a Hole" seems to be in the film solely so George Burns, who otherwise only narrates, can have a song. There's no attempt to connect it to anything plot-related, and it isn't diegetic either.
The scene where SPLHCB go up in a hot air balloon, and it's implied that a plane crashed into it (we see it from the plane's point of view and then an explosion), and the band is now on the plane heading towards Hollywood. What?
The final Deus ex Machina appears to have no explanation, nor is one asked or expected by the characters.
You can make a compelling argument that this entire movie is this.
Nightmare Fuel: Mr. Mustard's fembots are incredibly disturbing. The fact that their biggest moment is singing "She's Leaving Home" does not help.
One-Scene Wonder: Earth, Wind & Fire and Aerosmith only get one song/scene apiece, yet they're the best-regarded of the bunch. "Got to Get You Into My Life" has become one of EWF's signature pieces; some fans feel they perform it much better than The Beatles did.
So Bad, It's Good: Some sections of the film do have their fans – Steve Martin's take on "Maxwell's Silver Hammer" (lyrics not matching aside), Earth, Wind & Fire's "Got To Get You Into My Life", and the opening credits montage showing the original Sgt. Pepper and his band adapting to different musical styles from World War I to The '70s, for instance.