For most of the film, For the Love of Spock is about, well, Spock, and the international acclaim that it brought Nimoy and his family. Viewers are introduced to Nimoy as a hard-working family man who fought to make sure his children would always be provided for. We're also given great detail about how he conceived every single aspect of the character. Presumably this stuff is gospel for diehard Trekkies, though a packed festival audience didn't seem to mind reliving their favourite character's origin story. On a surface level, it's also about Leonard Nimoy, as we learn all about the various details of his work outside of the USS Enterprise.
When the film tries to get personal, it falls apart. Adam Nimoy is in front of the camera as much as (or possibly more than) behind the scenes, offering tales of life with his father and their various struggles. Because he presumably had final say into what made it into the film, however, the whole thing comes across as guarded. We know that they had brutal fights, but we never know why, for how long, or what caused them. When Adam reads a hand-written letter from his dad, it's undeniably moving but also saccharine and self-indulgent.
Similarly, both men's supposedly messy divorces are mentioned as mere footnotes amidst the sea of Spock imagery. A quick whiz through both Nimoys' Wikipedia pages suggest that there are likely some juicy stories being teased here on camera. Since Nimoy's son is the gatekeeper, however, he edits out the real warts that an outside party might've exposed. It would have been far better to avoid flirting with these tales altogether and stick to the Spock worship.
Worsening the tonal confusion, Adam Nimoy also adds a meta layer to the film by including clips from an episode of The Big Bang Theory wherein Sheldon is interviewed for Adam Nimoy's Spock documentary. Jim Parsons appears onscreen both as himself and in the character of Sheldon.
If you're looking for a well-crafted piece of cinéma vérité that gets into the nitty gritty of Leonard Nimoy's life, this is not it. The film is mostly unfocused, and more often than not it feels like you're watching a video that was assembled for a memorial service instead of a documentary. That said, until an outside perspective decides to come in and make a movie about Leonard Nimoy's inner life, For the Love of Spock works wonders as another piece of Star Trek fan service.