Character mistake: In the first scene, the Broslofskis are lighting their hanukiyah. It is the first night, and the lone non-shamash candle is on the far left side as they look at it. However, Hanukkah candles are placed in the hanukiyah starting from the right.
Continuity mistake: When Cartman is trying to convince Butters that a meteor is heading to earth, Cartman jumps on a Terrance and Philip chair when dangling the rock in front of the telescope. The letters T and P on the chair are pretty much across from each other and above Terrance and Philip's head before and after Cartman gets on/gets off the chair. When Cartman is doing his calculations in the next shot, the letters T and P on the chair are now in a different position on the chair and if you look under the letters you can also see that Terrance and Philip's head have also changed positions.
Continuity mistake: When Jimmy is talking about Christopher Reeve and Superman while the boys are on the ground playing with toy cars, Stan looks up at Jimmy and says 'Yeah that's nice guys. Were going to stay out of this one.' When the camera cuts to another angle, Stan's head is in a different position.