Cragen's Limited Advancement Opportunities (he's been at the same rank for almost 25 years) makes a lot more sense if you recall that, at the end of the first season of the mothership, he helped send the guy who had gotten him all his previous promotions to prison for corruption.
The whole show makes a lot more sense when you realize that it's not meant to be a realistic portrayal of the American justice system, but rather a Stealth Parody of its flaws.
Alternatively, it could be something of a Take That!, as the law system in the show isn't that much different than Real Life in some ways.
In the episode Padre Sandunguero, Barba loses what should be a slam-dunk case, implied to have failed because he was being reminded of his own possibly abusive father. The brilliance comes when you realize, between Barba clenching his fists during his cross-examination (a habit he admits he has when he thinks of his father) and the fact that Barba later says he doesn't understand how the cross-examination got away from him, because he's "known guys like this his whole life". In short? Barba lost a slam-dunk case because he thought he was questioning his own father, not someone's else.
From waaaay back in the series, the "Your Jew?" scene. When Fin says "Then I'd be your boy, John!", he's not just reiterating the validity of his own methods (basically improvised undercover), but making a joke on Munch being an old fart. Munch is using "my boy" as a particularly old-fashioned racist epithet, but in a modern context, your boy is your best friend. Of course Fin wouldn't object, it's only offensive if you're older than dirt.
In "Raw" a hostile witness pleads the fifth when asked to state her name for the court. Then we learn that she's an undercover FBI agent... so if she had given the name of her assumed identity she'd have perjured herself and possibly caused a mistrial.
This is pretty clearly stated to be her reasoning in the scene following The Reveal.
In "Parasites", the victim is described as a Gold Digger. When we later learn that another sister was being forced into prostitution to pay off a debt, it seems likely that she was like this in order to get the money to buy her sister's freedom.
One episode goes like this: Benson and Stabler suspect a recently-released ex-con that Stabler put away some time back for a series of rapes. For the first half of the episode, Stabler hassles the guy while looking for evidence to connect the dots. Finally, the suspect is found dead of a heroin overdose - just as they get word of another rape and attempted murder which had been committed while the guy was a corpse. After Stabler angsts for a bit, the second half starts up with Fin Tutuola going to meet an informant who gives them a lead on the real culprit. It was only after several viewings that I realized the episode was a Take That! against Stabler, and a Deconstruction of the show's own abuse of It's Personal. During the first half, Stabler does his typical Rabid Cop routine and fixates on this one guy he had a personal history with, convinced he must be their man. Meanwhile, Tutuola was offscreen, slowly cracking the case by doing his job.
Something that's always bothered me about the show is Benson and Stabler having the habit of jumping into cases that aren't theirs, especially when the FBI are involved; there have been several episodes where the victim or suspected perp are involved with an FBI investigation, and they either jump in or treat the FBI as the bad guys for not assisting their case. It took me a while to notice, but it's actually the opposite! 9 times out of 10, Benson and Stabler's interfering actually makes things much worse. In the episode where reoccurring agent Dana Lewis was raped, they went into such a frenzy assuming (incorrectly) she was in trouble/over her head/kidnapped after seeing her willingly enter a car that they indirectly caused several deaths (by being so obvious in their policework and frightening the baddies) and almost ruined months of undercover work. In another episode with a rapist in the witness protection program, if they had been content to let the FBI handle it, a shootout with the mafia that killed a dozen people would have been avoided not to mention the deaths of both the rapist and his father. There's no way this is an accident since it keeps happening; the show is very subtly showing either a Deconstruction of what really happens when you jump into a case over your heads... or an outright Take That! at the assumption time and time again that only the SVU detectives can solve the case.
There's an even more subtle brilliance to it. When they genuinely don't realize they're stepping in a federal case ("Raw"), are specifically asked to help ("Pandora", "Informed"), or go through proper channels ("Merchandise"), then the negative consequences of this type are usually avoided. But when they intentionally interfere (as in, without getting permission, or worse after being expressly told to back off), then the problems start to happen. And there's actually a good in-universe reason that this is the case; if they're working with the Feds, then they have the full big picture and everything is coordinated, but if they're working against the Feds, they're probably only getting a limited view of the total situation and the two groups are not coordinating with each other, increasing the likelihood of a Spanner in the Works situation for one or both cases.
This is completely subverted, however, with "Acceptable Loss", in which the SVU cops' decision to defy a "drop it" order from Homeland Security ends up being the reason that a terrorist is caught, because Homeland Security ended up holding the Idiot Ball on that case. But even then, it's pretty much just dumb luck that things work out as well as they do — it's easy to see how things could have gone wrong if a few details had been different.
Munch's love of conspiracy theories? Yeah, Beltzer was on an episode of The X-Files, playing a police detective heavily implied to be Munch (circa 1989). He didn't believe anything the three computer-hacking lunatics he picked up from a warehouse break in were saying at the time. However, if that was Munch interrogating the Gunmen (who go on to make their own tabloid), and this series really is in the same universe as The X-Files, then Munch probably subscribes to the Gunmen's newspaper (the lads encountered a lot of outlandish stuff that turned out to be true) and is just Properly Paranoid.
Greg Yates being an Expy of William Lewis may seem like a cheap move of retelling a story arc with certain tweaks. But if you think about it from another angle, this is where the Fridge Horror comes in: Lewis isn't the only one of his kind (psychopathic, chameleon-type serial rapists/killers who enjoy torturing and terrorizing victims in many ways, use their charm to lure in victims or get out of situations, are clever enough to mastermind prison escapes, will stop at nothing to get what they want, have been active all over the country for years, etc.). And who's to say it'll stop at Yates?
In the Season 12 opener, "Locum", a young runaway, Mackenzie Burton, is found at a train station in the company of one Erik Weber, an anti-pedophilia activist who claims he just met her and was trying to convince her to go home. Though Weber is initially suspected of luring the girl from her home via online chat, the detectives find another individual behind the screen name, and realize Weber really didn't have an online relationship with Mackenzie. Weber is released, leaving detectives and viewers with the assumption that he really was just trying to help, and the story takes off in a different direction. But the following episode reveals that Weber was actually a pedophile who raped two girls around the same age as Mackenzie. Was Weber actually trying to convince Mackenzie to go home, or was he preparing to make her his next victim?
Sheila Porter, the biological maternal grandmother of Olivia's son Noah, did a lot of cold things in her attempt to kidnap him. One of the coldest was cozying up to the man she had take the boy, her landscaper who she romanced and lied to about life as a family, only to leave him both as a fall guy and distraction. But her abuse of his affections and gullibility become many orders of magnitude crueler when you realize, if he got sent to a real prison, all the other inmates would care about would be that he took a child, and all the guards would care about that it was a cop's child. He was being set up to die a horrible death.
Often tends to crop up when things deemed unnecessary to the flow of the story are ignored by the writers. For example, it is never explained where a fifteen year-old boy who had slept with dozens of hookers was getting the money for the high-priced call girls he was seeking out.
It's implied his family is at least well off. He probably has a trust fund or something, like every other teenage suspect on SVU.
Also, Ariel is a genderless character in Shakespeare's The Tempest, who has been played by both men and women.
Elliot Stabler frequently bends or outright breaks the law to torture suspects (who more often than not turn out to be innocent and are often killed as a result of this), but for some reason the only thing that's brought up to internal affairs is the fact that he sometimes wishes rapists would die.
In the episode "Spectacle", the NYPD are lured into a false kidnapping case in order to facilitate finding the apparent perp's missing little brother. What is wrong with the brother that he can't just plead with the cops to go over his brother's case again, instead of say persuading the police to try and reopen the case?
They go over this in the episode. He did try to get the police to reopen the case, they just wouldn't bother.
What's more, he claimed to have gone to multiple precincts all throughout his adolescence. The fact that SVU found the younger brother after putting in some actual effort just goes to show that if other police tried harder, they might have been able to find Greg's brother a long time ago. Which is another problem of some cops. They just give up too quick.
In "Rockabye", why didn't Lauren just go to a different clinic? If she was that desperate, even after being told she had a fever, would she have really stopped at just the first clinic in the phone book?
The implication is that she believed that he was telling the truth (that she had a fever) and that other doctors would refuse to perform the procedure for the same reason. Also, she's fairly young and may have gotten mentally stuck on this one issue rather than parsing out the situation logically.
In "Parasites", the husband is stunned to learn that his wife is dead and that her twin sister has taken over. Fair enough, except. . .you didn't notice ANY changes in her? Her personality? Her domestic skills? Her bedroom skills? That she suddenly didn't know the names of friends, neighbors, etc.?
In "Risk," an infant dies after being fed liquid cocaine hidden in a liquid baby formula can. The baby's mother stole it from the couple she cleans for, who reportedly have a four-month-old baby themselves. Turns out the couple is smuggling cocaine across the border, using babies from the husband's corporate daycare as accessories to make it easier. But when the couple hands over the cans of formula, stored in their kitchen cabinet, for testing, only two of six were found to be cocaine. The rest were formula. Why keep them all in the same place? The techs couldn't tell until they removed the labels which ones had been tampered with, so why risk giving your client the wrong one? It's also not clear how long they keep the babies; the housekeeper was under the impression the latest one was theirs and the wife had been travelling with him several times over the past three weeks, so at least that long—why risk giving your product to the baby and a) now having less product and b) killing the baby?
The couple probably had some kind of system to tell them which was which (like "the ones on the left are real formula, the ones on the right are the product"), so they wouldn't have made the mistake, but the housekeeper did because she had no way of knowing that not all of the formula was safe. As for why they kept it all in the same general area, if they were having housekeepers and the like in, they probably wanted to avoid anything that could remotely make someone ask questions (or, worse, that a housekeeper would think it was a mistake and "put away" the supposed formula where there would be a possibility for confusion).
Also, when Olivia interviews the "mom", she indicates the police called her ahead of time, presumably to make sure she was warned as soon as possible. It's possible that they did keep the real and fake cans separate usually, but put them together specifically in anticipation of the cops' arrival so that it wouldn't look suspicious.