In the scene when Leela discovers and decides to protect the leech, Fry is to be seen standing behind her - but only a few shots later he regains consciousness and stands up after being crushed by on of the feminists.
When Fry gets to the secret society the first time, Hutch hits Fry's head with a bottle and tosses the unconsciousness Fry into the "secret entrance". While getting hit by the bottle Fry loses his tinfoil-helmet and it drops to the floor. But in the following wider shot of Fry the helmet is nowhere to be seen and Hutch hasn't picked it up. In the next scene it is suddenly mysteriously on the bench next to Fry.
(at around 1h 13 mins) Professor Farnsworth takes a five dollar bill out of his pocket, but when the camera zooms in on the bill it's being held by Hermes Conrad. When the camera zooms out again, it is back to being in Professor Farnsworth's hand.