Other mistake: Virtually all the text in the various articles and reports in this movie are fake. Look at the John Kramer article at the very beginning, even at first glance you can tell it's an article about pilgrims or something and has nothing to do with John Kramer. Also, when Staham is going through the articles he found on Hoffman's sister, you can very plainly see that every article (there are a few) is just the same typed out story copied and pasted into various formats. (This doesn't even require slow motion, just pay attention.) (00:11:45)
Other mistake: When Agent Strahm first starts investigating, he uses the FBI computer to look up Seth's name. He is heard typing many more characters, very quickly, than actually show up in the 'search' field on the screen. (00:29:20)
Other mistake: Seth is told that in 30 seconds the pendulum will drop low enough to cut his body and in 60 seconds it will cut him in half. We then see the clock start ticking. After Seth has crushed his hands, we see the clock - 46 seconds have passed and yet the pendulum hasn't cut him yet. (00:04:35)
Chosen answer: Assuming the woman in the bathtub was able to be moved safely the amount of blood gained from her, while still being helpful, would probably not be enough to save the final two survivors from self harm. Without the heart pumping blood you would only get the blood that was in her arm at the moment. You would have to lift her or raise her so gravity would get other blood moving to get enough. Which the final two possibly could have done, but stress of the situation clouded their judgement.