Fridge Brilliance: In the pilot, Annie's linguistics professor warns her not to join the CIA, that they'll just use her. Next season we learn he was one of their best operatives for decades. He would know how they operate.
Of course Joan thinks Arthur is cheating: she's his second wife, and their relationship started as an affair.
Also how Joan knows Arthur didn't cheat on her in Season 4. None of the signs were there.
From "World Leader Pretend", the reason Annie wasn't poisoned when she was eating out of the same bowl as her asset; her cover was as his translator, and so she spent the whole dinner speaking Chinese, with barely time for a sip of the soup...
Due to the way season 4 is structured, with secrets being slowly revealed that shed light on earlier episodes, it's absolutely brimming with fridge logic.
Case in point; Auggie joining Annie in Colombia. He says it's because he doesn't want her to have all the fun, but we're used to him having more of a reason for his actions. A few episodes later, we learn that Auggie thinks he has good reason to mistrust Teo and is trying to protect Annie from getting into trouble. He believes Teo got his wife murdered in front of him by delivering faulty intel.
In Auggie and Teo's meeting by the Jefferson Memorial, Teo leaves saying "Sorry about your eyes, man". Since Auggie blames him for his wife's death, it would be perfectly natural for Teo to apologize for what happened to her, until you realize that a) he had no part in the plot whatsoever, and b) the event wasn't even real in the first place. Teo is just refusing to apologize for something he never did!
If you think about it, this is the closest Teo can possibly come to saying that she isn't dead without actually giving up the secret...
Arthur calling Auggie out on having a relationship with a coworker seems to be about his dating Annie, until you learn about Auggie's past with Helen.