Early on in the episode, when Mal, Zoë and Jayne are breaking into the vault of a derelict carrier in space, we see Mal floating upside down looking at the spaceship's vault. The 'sticky' chemical that Mal asks Jayne for seconds later can already be seen on and around the vault lock.
Just after the crew escape from the Reavers using the 'Crazy Ivan', Wash is seen with his arm outstretched holding an imaginary steering wheel. This is explained by Joss Whedon on the DVD commentary; the makers had to pull the chair back in order to fit both Alan Tudyk and Gina Torres in the shot and Tudyk is simply miming steering the ship.
When the camera follows a man through a curtain to reveal the town of Persephone, an extra in white shirt, black vest and straw hat can be seen standing still to the left, likely waiting for the director to tell him to start walking. Several seconds later, the same extra is seen again behind Mal and Kaylee walking in the opposite direction he was just going.
When Wash is driving the ATV off the Serenity on Persephone at 18:00, you can see a crew member push to start it down the ramp and a hand grabbing the bumper to pull it off screen.
Zoe says to Patience 'awful lot of men to haul 3 crates' but there were 5 crates on the mule.