Continuity mistake: In the flashback to 1920, Kendra flips the calendar to October with a snowy mountain side picture. Later when she's talking to Carter about leaving, the calendar is now on September with a trail through the grass picture. It goes back to October when their son comes in.
Continuity mistake: In the scene aboard the Waverider when the crew discusses their discovery of the Oculus, the first two times you see Sara sitting on the Captain's chair from the back she's leaning forward with her elbows on her knees. When you see her from the front, though, she's sitting with her legs crossed and her right hand on the control panel, and in a following shot you can see her actually change her position and lean forward. (00:23:45)
Continuity mistake: While all the heroes are in front of the aliens ready to fight, the sun on the floor changes between shots.
Continuity mistake: When Ray talks to Alan, there are red binders behind Alan. The one on the end switches from being tilted and leaning up against the other book to standing straight up, depending on the camera angle.
Continuity mistake: When Sara, Mick and Zari get to the control room, Sara is wearing the sleeves of her coveralls down. In the next couple of shots she has them rolled up to the elbows, and then down again. (00:19:05)
Phone Home - S3-E4
Continuity mistake: When kid Ray opens the backpack, it's set so it's behind him. The baby Dominator comes out and takes a few steps forward, away from the backpack. In the next shot, he's barely a step away from it and it's now in front of kid Ray.
Continuity mistake: When Sara rejoins the crew at the end of the episode, Nate lifts his left hand to his face and hollers. In the next shot, he has his right hand to his face instead. (00:40:25)
Continuity mistake: After Leo makes his "heartfelt confession" to Mick and Mick says he wasn't listening, the glass skull on the desk moves position between shots without either of them touching it.
Hey, World! - S4-E16
Continuity mistake: After Gary says "it's part of the show" and turns to face the dragon, he lowers the microphone offscreen. Cut to the front, and it's up by his mouth again.
Swan Thong - S5-E15
Continuity mistake: During the fight scene near the end when Marie Antoinette tries to stab Mick he grabs her wrist, it keeps changing which wrist he is holding. When it shows from her point of view looking down he has her right, but from his point of view looking up he is holding her left.