Continuity: Kaylee has just put Simon's birthday cake down on the table when the explosion happens, but in many subsequent shots of both the table and the floor in the dining room, the cake is nowhere to be seen.

Continuity: One of the candles on Simon's birthday cake keeps blowing out and re-lighting itself between shots.

Continuity: When we see the flashback of Mal and Zoe first entering Serenity's cargo bay, just after Mal has bought the ship, there is a cable on the floor behind them. For a short moment, we see the cable being dragged over the grille right behind them, then the shot changes and there is nothing there at all; the only cable is much further back and lying at a completely different angle.