Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
Santiago is wearing 2 citation bars that are not issued by the NYPD. Also, NYPD regulations require that the American Flag bar be worn as the highest citation bar - something Santiago would have known.
Rosa insists she does not take selfies or photos of any kind and shows her phone's empty camera roll to Terry as proof. In Chasing Amy (2017) Rosa took a bunch of selfies and photos to show Jake dangling off a rooftop after he attempted to "Die Hard" off the roof to help Amy get to her sergeant's exam on time.
A great deal is made of Holt being back in his office and taking note of alterations Terry may have made to the decor, no matter how small (the figurine of Cheddar being askew by 5 degrees, the rainbow flag in the pencil cup leaning the other way, etc.). Holt was shown meeting with Terry in the office during his time as a uniformed officer. Someone as observant as Holt is shown to be would have noticed those sorts of things well before being promoted back to captain of the precinct.
After Doug introduces Jake to his criminal friends as "Sean" from prison, Jake says he just got out of jail after a 5 year sentence for elder abuse. Jail and prison are not synonyms. Jails are where people are held awaiting trial and for shorter sentences (less than a year), while prison is where they serve longer sentences. As a police officer, Jake should know the difference, but only Doug used the correct term.
Jake asks the suspect if the word "forever" in the password to Doug Judy's wedding website is spelled out, or if it's the number 4. He does not ask if the "and" in the password is the word and or if it's an ampersand (or possibly even just the letter "n" as the suspect pronounces it). He also fails to ask if there are any capital letters in the password; many sites use passwords that are case-sensitive and require at least one number and/or special character.