Opening scene killer uses a revolver with a silencer. Since the combustion gases are released through the chamber and not the barrel, a conventional silencer is ineffective on a revolver.
The medic at the end is bandaging McGarret's shoulder over his shirt, which means he never looked at nor cleaned or sterilized the wound.
When Danny Williams and Chin Ho are tailing Jack Houston (Sam Elliott), they engage in a conversation about not getting too close to his car and about his erratic driving, but a close-up of them through the car's windshield during this dialogue shows neither of them is moving his mouth.
During the meeting in McGarrett's office with Paul Hamilton, a shadow of the mic boom is visible on the wall above McGarrett when Hamilton is walking and talking.