When McGarrett is outside the state room door the handle and surrounding plate are broken/off, but when he opens the door, they are both fine/fixed.
When McGarrett and Danny confront the killer on the mountain, the green screen background is much lighter, showing their presence is digitally altered when you see their faces. When the camera switches to behind the characters, their doubles hair is styled differently and their stance doesn't match the actors when their faces are shown.
The bad guy is described as having quit his job in Michigan and gone on unemployment. If you voluntarily quit your job without a good cause in any state, you won't be eligible for unemployment benefits.