Deliberate mistake: When Agent Hoffman writes the letter to Amanda, he puts the envelope so her name is pointing down, yet when Amanda opened this drawer in Saw III her name was at the top. The director had to do this or it would have revealed Hoffman was the new apprentice all along.
Deliberate mistake: During the scene where Carlos and L.J. are searching the motel, L.J. sees a zombie which turns out to be a reflection in a wall-length mirror. L.J. shoots, breaking the mirror and realizing his mistake. But, if he had been standing in front of the mirror as shown, he should have seen his own reflection standing there as well. This was done as an homage to a similar encounter in the original game. (00:24:20)
Deliberate mistake: After Prof. Broom finally defeats the vampire countess near the end of the movie, many of her ghostly victims appear around the room. And, if you look closely, you can see that many of them look exactly like one another, revealing that the animators simply would repeat the same images over and over onscreen, to make the crowd bigger. (Confirmed in DVD commentary).
Deliberate mistake: So right before the containment team seal up the window with the tarp, the SWAT is shown having police dogs. The virus (which came from a dog in the first place) can be transferred through saliva. The SWAT obviously overlooked the fact that the potentially infected people who might escape could be bitten by the dogs.