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.
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.
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.