Shawn keeps "hypothetically typecasting" Gus as minor black characters in their favorite movies. This starts when he refuses to let Gus be "Goose" in Top Gun. That's because "Goose" is what Shawn's mother calls him.
In "Juliet Wears the Pantsuit" Henry says he's sorry to Juliette about how things went with her and Shawn. He's not just expressing sympathy, he's apologizing for his part in keeping up Shawn's lie. As much as he can with Lassiter present, anyway.
Shawn's general tendencies in Season 4 to get a lot of details wrong and generally come off as more of an Idiot Hero than before: he's a lot more prideful after capturing Santa Barbara's most notorious serial killer, and thus has an inflated ego. He then goes through a Break the Haughty thanks to Mr. Yin and his pride returns to pre-Yang levels in the following seasons.
How did Allison Cowley know that picture was of Yang and a young Shawn? She only knows Shawn from the news coverage of the Yin/Yang case, which wouldn't have included pictures from childhood. She couldn't unless Yin told her.
Remake AKA Cloudy... With A Chance Of Improvement... is widely regarded to be generally a terrible episode, does nothing to improve on the story and keeps the Flanderization present in later seasons. Which is the point. Shawn and Gus often complain about how movie remakes are usually bad copies of the originals, with pointless celebrity cameos and slipshod writing. It's one of the most meta jokes the show's made.
Lindsey from "Psy vs. Psy" claims to have picked up the information she provides psychically, but it later turns out that she was actually in on the crime she was investigating. Shawn probably figured this out because he was accused of being in on the crime he reported in the Pilot and claimed to be a psychic to explain his knowledge.
Shawn has a felony charge on his record (stealing his girlfriend's neighbor's car when he was 18), which makes him ineligible to become a cop. But it may also be part of the reason why Shawn hasn't held a stable, more permanent job—his arrest shows up on a criminal background check. Shawn certainly would have been terribly unhappy in such a job anyway, and he seems to have been perfectly happy with his lazy, quasi-nomadic lifestyle before returning to Santa Barbara, but it may not be entirely by his own choice.
In The Polarizing Express, Shawn has an internal argument with his own younger self, deciding it's past time he grew up. By the start of the next season, the show's traditional openings with flashbacks to Shawn's childhood have been phased out, and a few episodes start off with flashbacks to older Psych cases — a surprisingly meta bit of commentary on how Shawn is maturing after all.
In "Shawn Takes a Shot in the Dark," Gus plays a voicemail from Shawn for the detectives to give them the only clue to what had happened to Shawn. In this voicemail, Shawn mentions that he'd solved the case, but fortunately doesn't give any incriminating not-psychic details. But what if he had? Gus would have been forced to choose between saving his best friend's life by playing the tape, and keeping his secret by withholding potentially crucial information.
In "Juliet Takes a Luvvah", Shawn accuses a family man of being the killer, causing his wife to throw his belongings out of the house while he is dragged away by the police - all while his kids are watching. We don't linger on it for too long as he turns out to be innocent, but Shawn's mistake might have done permanent damage to that family.
In "Juliet Wears the Pantsuit", Laura's abusive husband Patrick comes to the house claiming to be Laura's date, and Juliet dismisses him (unaware of who he is) by telling him that Laura hooks up with a lot of guys. He comes back later in a homicidal rage. He probably wanted to kill (or at least seriously injure) Laura anyway, but Juliet may have accidentally provoked him into a jealous fury on top of that.
In "Tuesday the 17th," the initial case turns out to be a prank being pulled on Shawn. But those involved continued the prank after Shawn calls in Juliet, who is ready to shoot the killer if he appears...
