At the beginning of the film, Mike pulls his gun before Hannah says "She's been shot." The movie then goes into flashback mode and when the movie catches up to that moment, he doesn't unholster his gun until after Hannah's statement.
In one scene Hannah calls Norman to ask if he will go to Minnesota with her. She calls using an iPhone and you can clearly see her phone screen and that she is not making a phone call.
At the end, it was a day before Valentine's Day in Minnesota. But the trees had fall color in the leaves. February in Minnesota, trees would not have leaves.