When Pepita is walking towards Ernesto, her bottom left paw goes through her front left one.
When Miguel's abuelita catches him in the plaza with the Mariachi, Miguel pushes the guitar back. The Mariachi puts his hands up to keep his sombrero on and between shots, the guitar flips over in his lap. In one shot, the neck is on the Mariachi's right hand--the position Miguel, facing opposite, was holding it in--and in the next, the neck is on the Mariachi's left hand, as if the Mariachi was about to play it.
Despite Miguel going underwater twice, the old photo he is carrying is undamaged.
The villain that tries to poison De la Cruz in his movie is called "Don Hidalgo". However, the honorific Don is used with first names, while Hidalgo is a last name. The right honorific would be Señor Hidalgo (or Don Hisfirstname).
The Day of the Dead is called Día de Muertos in Mexico as it also shows on flyers and posters in the movie. Most characters call it Día de Muertos as well except for Abuelita. She calls it several times Día DE los Muertos.
The dead are obviously stuck at the age that they died. Imelda and Hector have spent several years in the afterlife at the same time, and Imelda has never realized that Hector is the same age as he was when he left her, clearly indicating the reason he never came back. She still wouldn't have known that he intended to come back and could simply think that he died shortly after deserting his family.
When Miguel is in the land of the dead after being thrown to the hole by de la Cruz his neck appears partially to have changed to skeleton but later when his coat is removed, it still has flesh on it.
When Miguel is playing his guitar and singing in the talent show in the Land of the Dead, it's not just his guitar that is heard, but other instruments including horns.
When Miguel returned to the Land Of The Living, and ran home, his family didn't ask him why he wasn't wearing his jacket.
Imelda refers to Miguel as her grandson, instead of her great-great-grandson.