Revealing mistake: In the scene when the main character is in the library on the internet, she goes to a couple of websites. When the shot shows the URL up top, it is C:\windows98\mydocuments\etc.html. Instead of actually searching on the web they used a premade html page and accessed it from their computer. It's simple enough to just not display the address bar in your browser, so I don't know why they let this one slip through...
Revealing mistake: When Rachel is racing to save Noah, she is trying to call him on her cell phone. There is a shot of two hands on the steering wheel as the car turns and then a cut to her holding the phone in one hand a split second later while she was talking the entire time, showing that the shot with both hands was a stunt double and not her.