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.
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 pun and 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.
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 proably 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.