Walter is examining the policewoman's brain, and finds damage to it from the villains' mind control techniques. He would be very unlikely to be able to differentiate such damage from the damage resulting from a self-inflicted gunshot to the head, especially from a 9mm bullet. He would, in fact, be rather lucky to find the brain all in one piece.
When the store clerk electrocutes himself, he places the key in the large slot on the outlet. This is the neutral connection that, unless miswired, would only have a few volts and not spark or cause the electrocution.
Walter explains that Peter's teddy bear emits a stream of audible white noise. White noise in audio terms is actually a particular signal with a fixed bandwidth which sounds to the ear like a high-pitched hiss. The teddy bear, however, emits a undefinable oscillating sound, predominantly in a lower frequency range.
In the beginning teaser, when the NY Police stop the 'kidnapping', they are armed with 9mm Beretta pistols. This is a mistake. NYC Police do not carry Berettas.
Tyler and Peter go to a strip club and have a meal. Strip clubs in this country would not allow a person who is obviously under 18 to enter and sit by the stage.