Continuity mistake: In the scene where Beldar has finished giving Gladys a driving lesson and they are sitting in the car, you can see that he has nothing on his lips. After Gladys kisses Beldar, you can see red lipstick. As the shots go from Beldar to Gladys and back, you can see the lipstick disappear and re-appear.
Revealing mistake: After Connie does the dive, for someone who has just been underwater she is hardly wet at all when she gets out and when she 'dries herself off' with the towel.
Plot hole: Michael McKean quits pursuing Beldar and approximately 15 years pass as indicated by Connie growing up, yet when you see McKean again and his assistant, they have not aged at all.
Continuity mistake: At the end when the girl sitting next to Beldar's wife keeps talking about great seats, you see she has pointy teeth, but at the end of that scene she has human teeth.
Continuity mistake: When Beldar arrives back at Remulak and is talking to the leader, the orange thing in the guy's hands disappears.
Visible crew/equipment: When the alien ship is lifting up the Coneheads in their red car and the two Federal agents with its magnetic gripper, as they get closer to the ship's lights, you can see safety wires, either for the car or the two men.
Suggested correction: What you're seeing is the car's antenna.
Continuity mistake: After Connie and Ronny's first kiss, Mr. Conehead goes outside to talk to Ronny and it is completely dark outside. When he walks inside, however, it's really bright outside.
Revealing mistake: The Subway sandwich that Connie stuffs all the way into her mouth is very cartoonish and fake looking.
Visible crew/equipment: When Beldar comes home from playing golf, he comes through the door from the garage. When he enters, he finds candles lining the floor. As he heads down the hallway towards the kitchen, look to the right of the screen and you can see a crew members hand on one of the stiles of the handrail of the staircase.
Other mistake: When the fighter jet says he has a missile lock, the shot cuts to the screen. You hear the characteristic beeping of a missile lock, but the screen shows only open sky.