Broken Base: Does a Family Guy episode about domestic abuse "work"? Some day that it's too dark to have anything worth gleaning or simply handled the subject incredibly poorly, others called it a bold move for a show otherwise known for its Comedic Sociopathy to prove it had heart by depicting a real-world issue so seriously.
For one, Brenda shows undying loyalty to her abuser, but neither give any reason why. In most cases, the victim sees past the abuser's abundant flaws to whatever made them fall in love in the first place, but it's just as often the abuser threatening to kill or withhold money from the victim if they leave, or the victim simply having nowhere else to go if they do. It's never stated that Jeff is doing either of these things or that he does anything that would make Brenda put up with his repeated assaults, so she just comes off as someone who's either oblivious to or who doesn't care about it.
Jeff, as with most of the antagonists on this show, is depicted as thoroughly stupid and cruel in a primal way, despite especially bad abusers usually harming people in crafty and very specific ways that they know will hurt them the most.
The most egregious of these is the title, "Screams In Silence," a common euphemism for domestic abuse and how it frequently occurs behind closed doors, where the perpetrator can do the most subtle yet effective damage, making it near impossible for the victim to get help. However, while it's true that police can't incarcerate abusers unless their victims file a complaint, Joe ignores the fact that Jeff is almost always ever seen beating Brenda up in plain sight, usually right in front of Joe's face, meaning he doesn't have to wait until Brenda files a complaint to do anything. It appears the writers were not even trying to portray the law accurately, as Joe later states that he can apparently arrest Quagmire for merely suggesting Jeff's murder, yet cannot arrest Jeff for publicly assaulting Brenda. However, considering Joe's remark that the police "can't get involved until it's too late," this might just be a very, very dark joke.
Finally, the gang decides that the best idea in the end is to simply kill Jeff, freeing Brenda. Cathartic as it may be, "getting rid of the bad person" doesn't automatically fix the problems brought on by abuse. Brenda is most likely severely psychologically damaged and, if left to her own accord, will immediately go to someone else who is just as bad.
Moment of Awesome: As much of a Flat Character as Jeff is and how wrong so much of the information on Domestic Abuse is in this episode, it's immensely satisfying to see Quagmire both surviving getting strangled (as he's sexually asphyxiated himself so much that it doesn't bother him anymore) by Jeff, then running down the bastard with his car and slamming him into a tree.
They Wasted a Perfectly Good Plot: Why does Brenda show undying loyalty to her abusive husband? Does Quagmire feel any remorse for objectifying women for years now that he sees it happening to his own sister? Will killing Jeff solve all of Brenda's problems, or will she just move onto someone just as bad? We'll never know, because nothing interests the writers of this episode beyond "abuse is bad."
Unfortunate Implications: Brenda is never seen again after this episode, meaning it is not known if she learned anything from her experience, turned her life around or ended up even worse with a child she was too mentally-feeble to take care of alone. In many real-life situations, the life of an abuse victim is not solved by the murder of their abuser, and they're more likely to end up with someone just as bad, if not worse.