The Military Police in the movie are real-life MPs from the Massachusetts National Guard. Some of them had responded in the week following the attack.
The film's script was a merger of two separate scripts. One was called "Boston Strong", and focused more on the action thriller side of the story. Another was titled "Patriots' Day", which was more of a factual drama. The final script was a mix of the two, which would have the film be both factually correct and would have some tense action to keep the audience involved and entertained.
Unlike in his previous collaborations with Peter Berg, Mark Wahlberg's character in this film, Tommy Saunders, is a fictional character created for the film. He's a composite of many Boston cops who worked the marathon, and aided in the manhunt following the bombing.
The interrogation team that interviews Tamerlan Tsarnaev's widow is part of the High-Value Detainee Interrogation Group (HIG). The HIG was created by order of President Obama, in 2009 and is housed within the FBI, but run under the auspices of the National Security Council. Their job is to interview terrorism suspects soon after their arrests, in order to obtain information of any further terrorism threat. The interrogation depicted falls under a special category, called "Quarles" interrogations, conducted when law enforcement believes that a threat to public safety still exists. Any information obtained during a Quarles interrogation cannot be used in a subsequent prosecution case. That is why officers were instructed to not Mirandize Katherine Russell when she was detained.
Normally, a player dropping the "F-Bomb" on live television would generate a fine and penalty from the FCC. Two days after David Ortiz's April 20, 2013 speech, the FCC announced that there would be no punishment for the speech. It's the only time the FCC has declined to punish that type of incidents. At the time, the FCC commissioner was Julius Genachowski, a Boston native.