When Peter first drags his feet across the carpet and shocked Chris, there is no rug seen on the floor. Next scene, the rug appears out of nowhere. Also the end of his sleeve changes colors from red to white.
When Lois is talking to Peter about what to do with the money they received from an 18th Century shipping token, Peter's hand is cut off at the knuckles, exposing the pillow behind.
Up to the point where Joe and his friends get banned from Big Pete's House of Munch, the front shots of the restaurant show a disabled parking space right in front of the building, with the sloped corner of the pavement around the restaurant next to it. After Joe gets banned, he and his friends return en masse and as they wheel across towards the restaurant there are now at least 2 spaces in front of the restaurant and the sloped pavement corner is no longer there.
When Peter adopts 30 puppies and tear his clothes off, his shoes come off mysteriously. Also, There's actually 32 puppies during this scene.
Chris, Stewie, and Peter are on the roof when Crippletron is formed. The next shot showing the full roof Chris has disappeared and is not seen until Peter is coming out of the hospital in a wheelchair.
When Ben Stiller tells Peter he must leave, the door in the background seems to be open. But when a close-up of Peter quoting, "Ah, all his movies stink.", the door is closed.
When Peter is chasing Meg after she spills water on him, the water on his shirt disappears.