(I answered "Yes" although I DIDN'T see a dog die in the movie. Explanation below.) I'm writing the following here, because this question is at the top of the page: The movie has an incredibly large number of blink-and-you'll-miss-it images (still and moving alike), many of which have no direct connection to Bowie. Images representing culture, historical periods, art etc. Literally any image or clip ever made could conceivably be featured in those lenghty "collages", and I might have missed any number of them. I can't say for certain if, e.g., a nuclear explosion is shown for a split second, or a pornographic scene, or a hanging, or someone giving birth... Therefore, I've personally answered none of the trigger questions, except for this one (I had to give an answer, and I chose "Yes" only as an attempt to direct people's attention towards my comment - I did NOT see a dog die in the movie) and the few I could confidently answer "Yes" to. And I want to warn you that you shouldn't be too trusting of the "No" answers in here, since other persons might very well have missed images as well.
I don't know for sure, but I have to choose an answer in order to write the following: Bowie tells that his brother came home from the army with strong symptoms of schizophrenia and spent the rest of his life in a mental institution. It's just me speculating, but the way Bowie tells it makes me think that the symptoms MAY have been set off by PTSD. I know nothing about the brother's story outside of what Bowie says in the movie - but the same will be the case with many who see the movie, so I choose to mention it.
To be honest, I can't remember everything that was shown, since much of the movie is a visual explosion of still images and film clips, so I can't say for sure whether we see a clip of a real suicide or not. But I'm answering "Yes" anyway, because we briefly see footage from a recreation of the famous photo "The Most Beautiful Suicide", which shows a woman who, having jumped from a building in real life, is lying dead on top of the car she landed on and thus damaged. In the clip, Bowie is "playing" the woman, lying on a similarly damaged car.
Bowie made the album "Black Star" while he was in the end stages of the sickness that killed him. Towards the end of the movie we see parts of an eerie music video that he made for the album, knowing that he was about to die and dealing with that fact through music and visuals. That made me feel sad, but that might not go for people who don't know about the end of his life. I actually don't think that his death or reactions to his death are mentioned (in spoken words, writing or pictures) in the movie, but I'm not 100% sure. Worth mentioning: We hear a recording of him saying at some point in his life that his life had been amazing, and that he'd do it all over again, so we're left with the impression of a life enjoyed and well lived, which is uplifting.