Visible crew/equipment: Just after Lockdown stabs Optimus in the chest with his own sword, Cade runs closer and shoots at Lockdown. He then hides behind some bricks. In that shot, the bricks are a broken wall that is two separate pieces. Then it cuts to a different shot as Lockdown returns fire at Cade, and now the wall is one piece. Not only this, but some random guy suddenly appears in the shot next to the wall and right where the explosion happens where Lockdown shot the wall. He is wearing the same color clothes as the wall and only visible for a moment. There was no other guy present until that moment and he just suddenly appears behind Cade and gets hit. It's presumably a special effects member setting off the charge in the wall by the looks of it and it detonated before he got out of the shot.
Continuity mistake: When the girls in the red jeep pull up to the mail boxes, Tessa gets out and says "almost time for a tan and get wasted." Another girl then gets out and throws one arm up in the air and cheers. From the front shot, you see that both her sleeves are still over her shoulders, and her hair is over her left arm, which is down. From behind and the sleeve on her left shoulder is down so her arm is showing, and her hair is now behind her back, with her pink bra strap visible.