Other mistake: In season 5 episode 7, Tony is talking about JFK, and said he was in grammar school when it happened. However, in this episode Tony celebrates his 47th birthday. He was probably born in 1960, so he would have been no more than 3 years old and not in grammar school when JFK was president. (00:26:36 - 00:38:02)
Revealing mistake: When Bobby feels provoked by Tony and gives him the first punch making him fall from the chair, Tony is then shown getting up. If you look very carefully, that shot actually shows Tony falling instead, so they reversed it to make it look like he was going to get up. (00:27:24)
Continuity mistake: After the fight between Tony and Bobby, Tony has a large blood stain on the front of his T-shirt and he passes out. The next morning Tony wakes up the blood stain on his T-shirt is significantly smaller. (00:32:00 - 00:34:00)
Revealing mistake: When Tony and Bobby are fighting at the cabin, Tony pushes Bobby against the glass door, which has a pre-break section visible right before Bobby crashes into it. (00:27:27)
Answer: It's a mafia thing. Taking food off another made man's plate in public view like that is comparable to the guy in Casino taking off his boots and putting his smelly feet up on the table.
It is not a "mafia" thing, it's basic manners and plain gross for another person to stick their fingers into a plate of your own food. Same with the feet on the gaming table scene in Casino. It's not a "mafia" thing, it's just rude and not something a person does in public.