- I know that Norma isn't the most rational person but why wouldn't she listen to Norman's perfectly reasonable and sensible suggestion to go to the police after the rape and murder? It was self defense and there is plenty of physical evidence to prove it. Abrasions on her wrists from the cuffs. Tearing and semen from the rape itself. There was no way that Norma would have gone to jail over it if she had just come clean about what happened.
- Paranoia and trauma. Norma has a long history of sexual assault and abuse. She came to White Pine Bay to start over and letting people know about this may ruin that chance ("who would want to book a room at the rape/slash murder motel?"), not to mention likely force her to confront her deeply repressed issues. Even if that doesn't make sense, keep in mind, like you mentioned, Norma isn't exactly known for being rational.
- Why was it so important to get the belt back from Officer Shelby even though it was on the boat that belonged to the dead man? How could Shelby prove that he found it at the Bates Motel in the first place? And even they did believe that was where he found it... how could he explain the fact he'd held onto it for so long?
- Wouldn't Norman's DNA or fingerprints have been somewhere in Blaire's home... other than just ... ahem... inside her? For example the teacup that he drank from right before sleeping with her? Isn't dusting the place for prints the first thing the forensic team would do in a murder investigation? Her throat was cut so there no doubt at all that it was murder. And Norman was certainly in no frame of mind to go back and make sure there was nothing there pointing to him. He didn't even remember sleeping with and killing her.
- It still doesn't prove he killed her. A split-second flashback clearly shows Mother washing the blood off of the knife, so it could be argued that (s)he did take certain precautions to protect Norman. Plus, White Pine Bay's not exactly the innocent and sunny town it appears to be on the first glance, given the numerous numbers of criminal activities and the implication that the majority of the police force is corrupt, so it's possible that people don't actually care enough to conduct a full investigation.
- Why on Earth would Romero let Norman go after he passed the polygraph? Yes his feelings for Norma complicated things and yes there was another more likely suspect who had also had sex with Miss Watson within 30 hours of the murder. But surely he would know that polygraphs are not reliable and that there have been plenty of people who have beaten them? By this point he knows there's something off about Norman and he's capable of violence. And if he's mentally unhinged enough to kill his teacher wouldn't he be unhinged enough to either convince himself it didn't happen or lie about it without it registering on the polygraph? Which is of course exactly what happened. Norman had completely repressed those memories up until just before he took the polygraph... and he was able to lie during it by rationalising that it was 'mother' who did it... not him
- Even if he suspects Norman is dangerous, he doesn't have any valid evidence to justify keeping him in custody. Plus, like you said, his feelings for Norma impact his action and, if you take a look at how Romero chooses to handle problems in his town, you can make the argument that he's actually not that great of a cop.
- What was the whole point of the Arcanum Club storyline? It seems to serve no purpose besides making us think Norman had killed another attractive woman and getting the hard drive into Norma's hands. Both of which could have done much more simply and without so much screen time.
- Filler and a means to set up a way to temporarily get Romero out of the picture without writing him off the show by having Norman kill him at the same time as Norma.
- I also don't really see what the point was in bringing Bradley back only to kill her off. Her story had already been concluded with her leaving town. I doubt many viewers had much of an emotional attachment to her character either as the writers seemed to be doing their best to make her unlikable and unsympathetic. They could have introduced another character who was sympathetic and had a real bond with Norman if they wanted an impactful death for the end of the season
- From a storytelling perspective, the Back for the Dead trope is a pretty standard writing tool intended to add dramatic twists. Whether audiences liked Bradley or not, one can argue that bringing back one of the original main cast members, and one of Norman's first and only friends, and then violently killing her was a sign that things were getting more serious in the overall story. From a more practical standpoint, it's likely that Nicola Peltz had some free time in between projects and was interested in briefly returning to the show.
- Why did Dr Edwards not put his foot down when Norman asked to leave? He's seen how quickly Norman can snap and become violent. He knows Norman has blackouts and he knows during those blackouts he 'becomes' Norma. He evens knows the blackouts started with Norman repressing traumatic memories of his mother being raped as he hid under the bed. But despite knowing that he has a very serious mental illness, is nowhere near completely better... and that his relationship with his mother is too close to be healthy, he just lets him go. Which of course leads directly to Norma's death and the events of Season 5. One decision destroyed so many lives.
- Dr. Edwards wants to keep Norman in the institution, but Norman still has his civil and human rights. If Norman launched a legal challenge, it would be on Dr. Edwards to prove to a court that Norman is a danger to himself or others. While Norman is suffering from DID, he does not appear to be dangerous. (We, the audience, know otherwise, but the good doctor does not - be aware of Fourth Wall Myopia.) Rather than getting into a legal fight with Norman that Dr. Edwards will almost certainly lose, and completely destroying their relationship in the process, Dr. Edwards instead settles for releasing Norman with the hope that he'll continue with his treatment and get better. It's the least-bad option he has.
- By the start of the season Norman's fantasy that Norma was still alive is starting to show some serious cracks... but how did it hold up for so long? From the bits we see that are not from his perspective the house is a complete mess as everything 'Norma' does is a fantasy in Norman's mind. And Norman has her corpse in the freezer so he has to be at least somewhat aware of the truth. Also how did he manage to fool everyone in town that things were fine? For two whole years? Surely at some point someone would have realized something was off? It seems like the situation should have imploded well before it actually did
- Norman compartmentalizes. The is a part of him that knows Norma is dead in the freezer, but a different part of him is convinced she is still alive. This is a real thing; the human mind has a capacity for holding two completely incompatible beliefs simultaneously and acting on both. As for the town, everyone is convinced Norma is dead and Norman is living on his own. Very few people would come into the house and for those that do, a single young adult male with a messy house is pretty standard. Norman is odd and lonely, but he's the local motel owner in a town filled with all sorts of unsavory characters. No one has any reason to pry.
- Also how the hell did Dylan go two whole years without knowing his mother was dead? Yes Norman fed him a lot of bullshit and he was busy being a husband and a father... but he didn't go back even once during those two years to make sure Norma was alright? Right before she died he was warning her that Norman was dangerous and that she was blind to think he wasn't. No alarm bells rang at all when he didn't hear from her?
- Dylan made it clear that his relationship with his mother wasn't working, and that for his own good he needed to leave. Why would he be surprised to not hear form Norma after that? This is the same Norma who moved across the country without telling him, and when he first tracked her down told him immediately to leave. Their relationship has always been broken.
- Why didn't Madeleine run like hell when Norman started dressing her up in his late mother's clothing? Yes she's unhappy in her marriage and Norman offers an escape from that... but you would think that would be a big red flag
- It's a little weird, but it's a big leap from "this guy's coming to terms with the death of his mother" to "this guy's gonna kill me".
- She's lonely, Norman seems like a really sweet guy and you could argue that the situation isn't totally creepy from a certain point of view. What is confusing (and kinda creepy) is why she appears to go along with it when she invites him over for dinner.
- We find out that Norman has started going out at night as 'Norma' and actually picking up men in bars for sex. Does he have homosexual tendencies he's suppressing or is it simply just another symptom of how much the 'Mother' personality has taken him over. He does seem pretty horrified when he realizes what he has done.