When Goren breaks into Bernard's back door by breaking the glass in the window, he reaches in and simply turns the door knob, without even turning the button lock on the knob.
It's never explained why Wally Stevens (the antagonist) does not have visitation rights to his children.
While his autism could explain why his marriage failed, few judges are not going to award at least partial custody to a father with no known criminal history and who has steady employment and a home.
However, during the investigation, the detectives reveal that Wally's wife took out a restraining order against him for repeatedly showing up at her house with flowers, asking her when she was coming home. Her new husband was a partner at a law firm and may have used the restraining order to appeal to a judge to limit or revoke visitation with the children.
When Goren is testing the noise made by a chain link fence, while it is opening, he taps his wrist and asks some police officers across the way 'Any of you guys know what time it is?', to which one answer with the time. From that, the detectives figured that the police officer heard Goren just fine. If fact, the officer could very well have deduced what Goren said merely by seeing him tap his wrist, which was done in plain sight.
Wally Stevens (Mark Linn Baker) is a short, mousy individual who demonstrated as being far along Asperger's scale. How he is able to incapacitate and kill Lance Reddick's much larger and more athletic Jack Barnard is never explained.
When the character of Wally Stevens is first shown, he is profiling the killer out of what seems to be savant hyper-deduction. Later, it is revealed that he "knew" the first discovered murderer and the second. He could have misdirected the investigation at that point (or, at least, not said anything useful), but he played it straight, instead.