When Kougami warns Ginoza not to try to understand how criminals think, it seems like nonsensical advice to give to a detective whose job it is to track down and apprehend criminals... until you learn that Kougami was an Investigator who was demoted to Enforcer when his Crime Coefficient got too high, and you remember that just being involved with someone with insane or criminal tendencies can affect someone's own Psycho Pass hue and Crime Coefficient.
Why was Masaoka allowed to get away picking up Gino and flinging him around? He's his father.
Gino always tells Masaoka and Kogami to go with Akane. Given his connection with those two it makes a lot of sense.
Furthermore, consider that Masaoka and Kogami are the oldest Enforcers on the team, with the most experience not just as Enforcers, but as investigators as well. It makes sense to assign them to Akane, who is still a newbie.
In episode 12, Yayoi is unable to shoot her former bandmate-turned-criminal because her Dominator is locked. This is not explicitly pointed out in the episode, but sharp-eyed viewers probably weren't surprised, as they may have noticed when Kougami gave her the Dominator, it did not give her the standard "you are a registered user" audio notification.
The English word "Psychopath" is pronounced "Psychopass" in Japanese. Besides the obvious pun, the criminally asymptomatic brains that make up the Sibyl System are arguably psychopaths, if the examples of criminally asymptomatic people (Makishima, Touma) in the show are similar to the average criminally asymptomatic individual. Maybe the Sibyl System brains thought this to be a cruel joke, by implanting Psycho-Passes in everyone, everyone is a "Psychopath".
Masaoka's has an Artificial Limb for his left arm. His son, Ginoza, loses his left arm at the end of the series.
The Sybil System works by judging the citizens' thoughts and intentions rather than their actions and results. When Akane learns of the Sybil System's true form, she chooses not to expose it. She judges the system by its actions (keeping the populace safe) rather than its inner workings (which are the definition of criminal). In other words, by "accepting" the Sybil's existence and choosing not to punish it, she rejects everything the Sybil System stands for.
Near the end of episode 21 when Masaoka is dying, he tells Ginoza that his "eyes... look just the same as mine did..." In episode 22, as Tsunemori and Ginoza are returning from visiting Masaoka's grave, Tsunemori asks Ginoza if his glasses were just for show. Ginoza replies, "I don't like how my face looks, especially my eyes. But I don't care about that anymore, so it didn't seem to matter." Ginoza has come to terms with his and his father's identity.
When Makishima was killing Yuki, his Crime Coefficient dropped down to near zero. Since in this Crapsack World, a person's soul is measured by the Sybil system, it's safe to say that Makishima is a Soulless Bastard.
It's stated in episode 12 that it is very rare for someone who is put in a rehabiliation center to reassimilate back into society, so those arrested will most likely be stuck there until they die (by execution if their crime co-efficient gets too high) or become an enforcer if they are eligible and choose to do so.
In episode 13 it's stated that there are rare cases where the result of the personís cymatic scan do not match their criminal psychology, they are called criminally asymptomatic. Some cases of criminal behaviour cannot be judged by Sibyl see Makashima. But by the same merit surely there must exist other 'criminally asymptomatic' people who are judged as 'latent criminals' by Sibyl but aren't because their scan doesn't match their criminal psychology.
There's also a very heavy hint that Akane of all people might be one of those types like Touma and Makishima, what with her CC going down just as she decides to hunt Makishima by any means necessary.
In episode 14, why did nobody try to save the woman being murdered, instead watching and even video taping the crime? Because the system has made it so that they don't even know what crime is. To them, this is something that they have only heard about. If Sybil has become their eyes, then they are truly blind to actual horrors. Really says something about the society the show is presenting.
This is also due to the Bystander effect, which was referenced on the main page. This doesn't make it any less concerning though, as it means that situations like these happen in real life as well
Also in episode 14, The helmet wearer got the psycho pass of the person with the lowest rate nearby. When it was only Masaoka and Kogami near it got Kogamis at 280. Then what do Masaoka have?
Masaoka's only seems to be high because he hates the Sibyl System, as talked about between him and Ginoza once. The Sibyl System probably sees him as a bigger threat because Masaoka wants the Sibyl System flat out destroyed while Kogami just wants vengeance on Makishima (which although killing Makishima could be considered a good thing, due to his tendency to create murderers, it would still be considered a crime to kill someone).
When Yayoi was in the mental facility, her order request for guitar strings was denied every single time. On one hand it could be because as Ginoza points out, artists have a higher tendency to cloud their Hue. The other reason (and the more horrifying in hindsight) is that they were seen by the facility as something she could harm herself with, like strangulation.