Detective Stone said that they had run the shell casings at the crime scene for ballistics and DNA. (This is only hours later but, unbelievably, they already have results.) Remy picks up a pen from the desk (without wearing gloves) and uses it to pick up another casing from beside the body. Presumably, the police would already have collected them all.
When snipers have sights on a shooter and the person puts the gun to the person's head, they are trained to stop the threat to the hostage's life. Hollywood likes the drama, but snipers can't afford to play that game when a hostage is in danger.
A Massachusetts State Trooper introduces herself as "Officer Marshall", however state police use the term trooper, not officer. Officer is used to describe local city police.