Logan tells Arden when he was shot the bullet exited his back. In the flashback after he is shot there is no exit wound in the back of the shirt he is wearing.
The detective tells Arden there will be a problem getting a restraining order due to her signing the release. This creates two problems- first, you cannot legally authorize someone to break the law- such as kidnap you or as a more extreme example murder you. Next, the release was part of a contract for services. Arden had clearly terminated these services by the time she contacted the police, so it was no longer legally in effect.
The detective first responds to the warehouse and later to the forest for a known violent kidnap/homicide suspect and does not call for backup, such as an officer that would be closer than her.
Logan is supposedly a highly-trained self-defense expert, yet at the end when he is in the forest with the gun, he points it out in front of him at arms length. Trained shooters in that situation hold the gun at a ready position close to their body.