Continuity mistake: While trying to restart the engines after the ship is hit by the nuke's EMP, Chandler is checking the fuses while Chung is going through his checklist. There are only five visible fuses in the six available slots in the panel that Chandler is checking. After he gives the order for Chung to "give it a kick-start," the slot which previously had no fuse now does, only for it to shoot out from the start attempt.
Revealing mistake: At the river to cross over to Mt Weather, the vine used to swing across the river is just a standard rope, camouflaged. You can see it best when Finn recovers it after Jasper has jumped.
Visible crew/equipment: When Molly walks into the "memory lane" tent at the carnival, four shots in we can see the reflection of a crewmember (moving dark silhouette) on the glass display beside the entrance. Then as Molly turns the crank and looks into the Mutoscope, in the wideshot we can see a crouching male crewmember hiding behind the case, at the left side of the screen. (00:28:15)