The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When the Fantastic Four are first shown on Dick Clark's show, Johnny is seated on Sue's right and Reed is seated to her left. A couple of shots later when Dick Clark is telling them what his telethon viewers really want to know, Johnny and Reed have swapped sides. (00:02:06)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When Sue is holding up the book for Dick Clark, her right hand is on the bottom of the book on the spine side, and her left hand is in the upper right corner. When the shot changes, her right hand is suddenly closer to the top-left corner. (00:02:18)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When Sue turns invisible for the first time, Ben Grimm's hair alternates between being gray and auburn. (00:07:46 - 00:09:08)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When Dick Clark walks back over to his desk after giving instructions to the camera operators, Sue is shown sitting equidistant between Johnny and Reed. When the shot changes, she is suddenly sitting closer to Reed, and Johnny is nowhere to be seen. Reed also suddenly has blonde hair. (00:15:03)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When Puppet Master is putting the Thing figurine inside the dollhouse, the windows on the bottom level are smaller than his hands. When the shot changes, he's suddenly able to fit his entire head and right shoulder through one of the windows. (00:15:41)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When Johnny slouches down on the couch, the black 4 on a white circle on the chest of his uniform suddenly becomes a white 4 on a black circle. (00:16:33)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When Thing first walks into Puppet Master's house, the doors are gray. When the shot changes, the doors are blue. (00:17:00)
The Origin of the Fantastic Four: Part 1 - S1-E1
Continuity mistake: When the shuttle crash-lands back on Earth, it is twilight. When the group exits the shuttle, it is suddenly dark outside.
Suggested correction: There's no way of knowing how long they were in the shuttle after it crashed, what happened to them, or what they might have been doing. It seems it's just meant to show a passage of time.