Corrected entry: Ernesto de la Cruz was exposed in the afterlife as a fraud, but the movie went on as if he was also exposed in the current present life too. The boy could have mentioned it, but would he really have been taken serious on the subject there? Ernesto would have gone on and been idolized in the real world, unfortunately.
Corrected entry: After Hector plays for Chicharrón he drinks a shot of tequila, it should fall through his skeleton and hit the floor, but doesn't.
Correction: The skeletons are also able to move and talk without muscles, tendons, or tongues and they have hair, eyes, and mustaches. We even see some eat at the party and one guy blew fire (which requires spitting out alcohol from your mouth). There's no reason to think a drink would spill out when they're able to do all these other things.
Corrected entry: After Coco died Hector should be forgotten and disappear from the land of the dead because his daughter was the only person who knew him in life, even from pictures according what he said to Miguel about Chicha.
Correction: According to the rules of the film, it's not that someone had to have known you in life, it's that you are remembered. That's part of the plot; Hector will disappear because Coco is the only one who remembers him. When hearing her father's music "brings her back" she starts telling the family stories about him, so he'll continue to be remembered.
Correction: In addition, Chicharron has already been forgotten. He can't come back just because Miguel remembers him from the land of the dead.
Corrected entry: While the pizza planet passes by Miguel's house, there is a frame on the wall that disappears between shots.
Correction: It's not an error, new shot is from a different perspective and the objects on the wall are simply not visible.
Corrected entry: Frida's costume was in custody in the security office, so Hector couldn't use it to get in to the de la Cruz party.
Correction: Given that Frida likes Miguel for helping her, she could have been convinced to give Hector the costume to help him.
Correction: It's mentioned in the movie that Coco's letters from her father contained all of the songs Ernesto put forth as his own, proving he stole the songs.
I'm sorry. That wouldn't prove anything to anyone other than Coco and maybe the family directly.
Nevertheless, that's the explanation given in the film. It's been a year. More than enough time for them to investigate the letters.
To add a bit more to the above explanation... Ernesto de la Cruz would likely have fabricated a back story to support his claim of authorship of the songs, which the letters to CoCo would have refuted, leading to scrutiny of the author.