Continuity mistake: When Jenny arrives at Oliver's parents' home, her hair is stringy and separated, but when she walks through the front door, it is brushed.
Visible crew/equipment: When Comicus and his entourage are on the road to Judea, the tire tracks of the vehicle carrying the camera are blatantly clear in the lower part of the picture.
Continuity mistake: At the end of the film the plane they are initially flying on is a typical passenger plane, but when the Muppets are thrown out, the plane is one used for skydiving.
Other mistake: Towards the end when Janet, Brad, Oliver and Betty are singing "We're going to do it anyhow," as they are dancing down the aisle, Betty very visibly trips and grabs Oliver to stop from falling over.
Continuity mistake: Set in the 1930s, Steve Martin is teaching a class of grade-schoolers in one scene. This would only be picked up by Canadians, but one of the many flags on the wall is the new (as of 1965) Canadian Flag - Red Maple Leaf with two red panels on either edge.