Revealing mistake: At the start, young Chas takes a sip of drink in his office. He doesn't take anything or even pretend to swallow.
Visible crew/equipment: In Royal's bedroom, when Henry exposes Royal's false claim to have stomach cancer, Royal exits the room by the left door. A crew member is standing in the background behind that door, apparently having a cup of coffee. (01:01:35)
Continuity mistake: When Royal meets Ari and Uzi for the first time at the 375th St Y, we first see Ari and Uzi from far away, exercising, and Buckley the dog is standing up wagging his tail. It then cuts to a close up of the boys, still exercising, and Buckley is asleep on the ground.
Continuity mistake: When Ben Stiller throws Owen Wilson over the wall you can see that Owen would land close to, and parallel, to the wall on the other side. A few seconds later Ben jumps over and from his direction you can see Owen is now perpendicular to the wall. It is unlikely Owen would have taken the time to rearrange himself after a 6 foot drop.
Continuity mistake: Margot is in Richie's tent in the Tenenbaum house. She drops a needle on a vinyl LP at the start of a track, about 2/3 way into the disc. This track plays throughout the scene, and when the song ends, this visibly coincides with the end of the track (on the disc). However, after the change of camera angle (which enables one to see the individual tracks on the LP), the track playing is only the second track on the disc: ie starting less than a third of the way into the disc.
Continuity mistake: When Royal asks Chas if he's still got the BB lodged in his hand, Chas holds up his left hand to show him. In the next shot where Royal pokes at the BB, Chas' hand is coming from Royal's left; when Chas puts his hand down, he's still sitting to Royal's right.
Other mistake: After everyone finds out Royal does not have cancer, Chas storms over to the yellow phone. You can see Chas is making movements as though he is pushing buttons on the phone to make a call, and there are accompanying button pushing noises. However, when he's finished, you can see it is a rotary dial phone.