Continuity mistake: When they jump in the pool, they drop the guitar. When they jump out their guitar is no longer in the pool.
Other mistake: When Miguel is singing "Un poco loco" on stage, he goes out of range of the mic, but his voice is amplified.
Continuity mistake: Miguel is thrown into the pit and lands in water, being completely submerged. But a couple minutes later when Hector mentions Coco, Miguel pulls the family picture out of his pocket, and the picture is totally dry and showing no effects of being submerged.
Continuity mistake: When Mama Imelda is singing on the stage and in the shot where she runs towards Miguel and Héctor, you can see several security guards on the stage attempting to apprehend her. However in the next shot that shows Ernesto grabbing her hand, there are no security guards visible. Three of them reappear briefly (the shot lasts about a second but you can see them) but they disappear for the rest of the scene. (01:23:05)
Continuity mistake: When Miguel is using a bottle to make some music the fruits in the background change between shots.
Continuity mistake: When Hector confront Ernesto just before he gives Miguel his blessing, he peels off the Frida disguise. But his beard on his chin is missing. It shows up in the next scene. (01:04:23)
Other mistake: Miguel was drowning in the swimming pool in De La Cruz's party but when he was thrown in the pit he managed to swim out of it.
Answer: It is never really explained in the movie, but we could assume that whenever someone dies they keep whatever items they had on them. Hector may have had the photo on his person when he died.