Continuity mistake: Bobby takes their red Charger and plows it through a locked gate. You see in the close up a lock on the chain, but it cuts to a further shot just as the car hits the gate and the lock is in a different position for the brief moment it can be seen. (00:06:50)
Continuity mistake: When the two sphere halves are coming together, and they generate a slow motion field in the R.I.P.D. building, everything is moving at extreme slow motion. Except the ceiling fans, they seem to be working just fine.
Continuity mistake: Roy picks up the solid gold cross in the house and throws it onto his shoulder, Roy is a big man and he struggles to do this due to the size and weight, but near the end of the film the same gold cross is handed to Hayes and there appears to be no weight to it - also it is considerably smaller.
Continuity mistake: When Nick and Hayes are fighting, and the time leading up to it, the Soul gun is using limited ammunition, but earlier in the movie when Nick was shooting up a building to hit Polaski he fires more shots and does not reload or run out. (01:20:00 - 01:20:50)
