Stupidity: Cooper dug an underground tunnel from his house to a neighbour's house? And no one in his family noticed him hauling away tons of dirt over the course of probably years? Or wondered what he was doing spending hours by himself under the house?
Suggested correction: He could have done it slowly over a long period when his family was away (wife at work or visiting her parents, children at school/kindergarten, etc.). It is also possible that there already existed some cellar that only he was aware of, which would greatly reduce the workload, and he could have stored the dirt there until he got a safe moment to take it away. Complicated, but not impossible.
Plot hole: It would have been impossible for Cooper to get out of the limousine that he was driving Lady Raven in and change clothes without anyone seeing him, because the limo was surrounded by her fans at that very moment.
Suggested correction: Lady Raven's fans did not know what was going on, so they would not stop him from getting out of the limousine and disappearing into the crowd. Fans thought he was her real driver.
Stupidity: The behaviour of Lady Raven and Cooper in the bathroom scene does not make any sense. They both reached an obvious point of no return the moment she stole his phone, and he violently chases her. Cooper is never going to bounce back from his actions in the eye of his daughter, but he gives the singer about three and a half minutes of time (on screen, supposedly way longer) to do the most counter-intuitive actions possible, something she couldn't know she would be allowed to do, since obviously a beast of a firefighter like the maniac she is dealing with could, should, would have kicked that flimsy door open in no time. Nor could Cooper know that she wasn't just going to call the police on him right away after breaking or throwing away his phone. Which was all she needed to do.
Suggested correction: Cooper likely hoped that he could still somehow save the situation when he got his phone back, and banging at the door and loudly demanding his phone back was the most he could do in front of his family without looking too crazy and suspicious. Lady Raven created a situation he had not foreseen, and he was obviously panicking but still hoping that he could come out of this. Kicking the door open would have looked too crazy.
Plot hole: The movie establishes that the FBI has a list of suspects thanks to security camera footage from the area where the victims were found. "A red headed man, two African Americans above average height, a white haired man." Then, the zinger; "a man in his 30s with a tattoo of a rabbit or an animal on his right arm", which of course is our guy Josh Hartnett. We see the tattoo, and it's a little doodle of a sheep, about a couple square inches big, below his wrist. That doesn't really make sense; if they have security footage with that level of detail, one wonders how could the rest be so vague. The next entry mentions "a male with a scar on his jaw", which is even more absurd. Either the security cameras picked those details up along with the suspect's full appearance and mugshot, or they just can't know with such certainty (if the suspect was masked or concealed in any way, then they would know for sure it was the killer and wouldn't be chasing people with wildly different appearances).
Suggested correction: I don't think you're wrong, but I think most of the FBI chief's voice was hallucinated. They shared the same voice; he was imagining her giving tips to the police, etc., etc.
