This One Time at Space Camp... - S4-E18
Plot hole: When Dr. Hughes is racing to save Allison when he thinks he is Carter from the events that happened in "I'll Be Seeing You" Henry says he is racing for a cliff, and that the cabin was just a hologram. But in the episode the Cliff was the hologram disguising the cabin. Henry even commented in that episode that he did not remember a cliff being there.
Factual error: At the dance in 1947, a US flag with 50 stars is visible.
Continuity mistake: When Andy pushes Jack out of the way when the F.T.L. is malfunctioning he is pushed into 2 stacks of crates, they are seen all falling away from him. The next shot of him he is just falling against the crates and one of them falls on him instead of away from him and the other stack stays where it is.
Revealing mistake: When Carter and Jo talk to Fargo in the cage, the first clip has him floating in mid-air. Then, the force field expands. It cuts away, and when it goes back to Fargo, they didn't remove the rig he was sitting on to make him float in the first shot.
Continuity mistake: When they are talking about the power supply Jack has his hands on his hips, except for one shot where they are crossed.
A New World - S4-E2
Continuity mistake: At the end of the previous episode, when Jack comes home to find Tess there, Tess says "I thought you'd never get here" and then asks if he wants a drink and goes to the kitchen. In the beginning of this episode (which is suppose to be the same scene) she says "I thought you'd never get home" and Jack replies "you're not in Australia" and then Tess asks S.A.R.A.H. to make him lunch.
Other mistake: When Zane and Andy get on the elevator, Jo is there to zap Andy. We see Andy start to fall backwards, and then we hear a thud as if he fell to the floor. When the shot changes, he's propped up against the wall. But he was standing too far away from the wall to land against the wall in that position.
Continuity mistake: Before the launch when the countdown timer speeds up, the timer shows 21:09 and counts down to 21:00 then goes up to 21:59 instead of 20:59. Later the timer is at 18:08 and in the next shot of the timer it's at 18:18.
Continuity mistake: When Jo is waking up from her surgery, both hands are on her stomach. The shot changes, her right hand is on her chest and her left hand is off her stomach.
God Is in the Details - S2-E10
Character mistake: When Diane quotes the scripture, she says "Revelations." However, it's just "Revelation." Someone as smart as her who has read the New Testament (or heard it quoted) would know the correct word.
Continuity mistake: When Sheriff Cobb loses his leg, Allison looks down and we see his leg back from the edge of the hole. The camera moves and we see his leg right next to the hole.
Continuity mistake: When Henry stops the countdown to launch, the time stops at 5 hours 13 minutes and 32 seconds. Later after the events at Cafe Diem the clock is stopped at 5 hours 13 minutes and 11 seconds.
Continuity mistake: Issac slips and falls on Jack's melted jeep - the shot changes and we see him fall again.
Factual error: Zane used ULF (Ultra Low Frequency) to communicate with Henry and notes he can "only send numbers." This is a reference to extremely low bandwidth of maximum 300 Hz transmission. However, later Henry magically creates an upgrade that allows voice communication - not possible with ULF. Also, no way Sheriff's old radio would pick up ULF band communications in the first place.