Other mistake: At the end of episode 2, Robin escapes from the Visitors into the wilderness. In episode 3, she's seen in an internment camp with no explanation as to how she got there. She is also wearing different clothes. She later escapes the camp along with other resistance members. Then at the beginning of episode 4, she is back alone in the wilderness, wearing the same clothes as at the end of episode 2. My guess is that episode 3 was added as an afterthought. (00:01:30)
Plot hole: Ham Tyler doesn't recognise Kyle Bates even though he met him in the internment camp in episode 3. Ham also makes exactly the same remark about Nathan Bates in both episodes. (00:10:30)
Revealing mistake: When Ham drives the van through the road barrier, the pieces fall off very easily considering how slowly he was travelling. In the next shot it is shown that the remaining barrier sections are both split vertically, revealing that they were sawed in the same direction beforehand, then the 'broken' pieces loosely affixed before the collision. (00:32:50)
Visible crew/equipment: When Diana and Lydia are walking in the mothership corridor there are two things to look out for. When Lydia first starts talking a section of the whitescreen appears in the top right of the picture. Then a couple of seconds later the shadow of the camera appears on the door to her left. (00:07:05)
Continuity mistake: When Mike is about to kiss Diana, he puts his thumb on her chin. Then in the next shot his thumb is away from her chin. (00:28:20)
Visible crew/equipment: When Sean enters Mike's bedroom after the capture and says 'dad, you're awake', the boom mike is reflected briefly in the wall mirror. (00:18:40)
Continuity mistake: When Diana is about to eat the white mouse, Donovan puts the tray of mice down on the bed, then in the following shot he puts it down again. (00:28:10)
Continuity mistake: When Ham Tyler is fixing the van in the garage, there is sunlight shining on him when the camera is facing out onto the street, but there is only normal daylight when the camera is facing inside the garage. (00:24:25)
Continuity mistake: When Mike pulls the necklace off the fake Julie, Julie's head is lying at a slightly different angle than when she changes into Lydia. (00:39:20)