Some fight-or-flight effects on the body include tunnel vision and auditory exclusion, also known as "tunnel hearing." These effects not only can affect your ability to react properly to the threat, they may cause you to harm innocent bystanders or yourself.
I had a shiba inu dog. Shibas are extremely good hunters. If a shiba sees a rabbit, it will pursue the rabbit until it catches the rabbit. The sihiba will not response to anything during its pursuit, not matter how well trained. It sees and hears on one thing, the rabbit. One problem is that the shiba will run into traffic or over a cliff if the rabbit does the same; this can be a problem for the shiba, and the owner. Once the human body is set up to run or fight, its only concern is dealing with the threat, either by escaping or by eliminating the threat. We still see and hear everything around us, but it does not matter, the cortex of the brain screens out anything that does not pertain to the threat and we do not react to it.
With tunnel vision, you lose your peripheral vision and depth perception, you only see that which is directly in front of you and you may not see what else lurks behind the foremost threat or any other threats on your flanks. Another problem is that you lose sight of your own arms and hands, which can mean that they may not be where you expect them to be when you take an action. If the attacker has a weapon, you may fixate on the weapon, and not see any other threats.
Along with tunnel vision comes tunnel hearing. The hearing is directed at the threat and any other sounds seem muffled and distant. You may not hear shouts that warn of danger, or such things as the commands of responding police officers.