In the beginning of the film, when we are introduced to Margot Tenenbaum, the narrator states that she was 12 years old when she first ran away, and that she ran away a second time 4 years later, when she lost half a finger, making her 16 years old at the time. Later in the film when Margot is telling the story of her lost finger to her nephews, she states that she was only 14 years old when she had run away.
When Margot and Royal are watching the Peter Bradley Show together in Ritchie's room, the door to the hallway is clearly open. However, when Ritchie enters the room from the hallway, he has to open the (now fully closed) door.
When Kumar and Royal are in the game closet, there is an shot of one of the Dalmatian mice running across a shelf filled with games. The games in this shot are arranged in a completely different order than in the rest of the scene (and the previous game closet scene).
When Richie is seated and waiting for Margot to pick him up at the passenger ship terminal, the shot shows several sailors wearing dress white uniforms walk by behind him. After a shot of Margot, the next shot of Richie shows a porter behind him pushing a baggage cart. The sailors are nowhere to be seen.
When Richie is in the bathroom trying to kill himself, we see him cutting his hair and shaving. As he cuts his veins, we see he did not finish cutting his hair fit or shave completely. When he wakes up in the hospital, his head and facial hair are fully shaved.
When Royal takes Ari and Uzi on their adventure and they are riding the garbage truck, the opening shot shows a side view of the trio. In this shot, Royal is not wearing his cap in following shots, Royal is wearing his cap backwards.
During the tent scene, a The Rolling Stones record is playing. The two songs played consecutively are "She Smiled Sweetly" and "Ruby Tuesday". It is clear that no tracks are skipped. Although both songs are on the Rolling Stones' album "Between the Buttons", these songs have never appeared consecutively on any Stones' release.
It's said that Mordechai's feathers have gone white due to stress. The misconception that stress turns human hair white is because stress can kill off living follicles, so that the darker hair falls out leaving just the white hairs behind. It's probably different for birds.
After Royal has Etheline sign papers, the notary is supposed to stamp them, but it is visibly obvious that the notary is just lifting his stamp up to the papers but not actually pressing down or stamping anything.
The goof items below may give away important plot points.
When Pagoda stabs Royal outside the house, we see him holding the knife in his right hand as he opens the door with his left. When it cuts to a wider shot of him stabbing Royal, the knife is in his left hand.
During Royal's funeral scene, Henry Sherman's son Walter, a U.S. Navy Lieutenant, has fewer medal ribbons on his uniform than he did during the wedding scenes earlier on in the film. In the earlier scenes he has 6 medal ribbons, in the funeral scene he only has 4.