Maura is wearing different eyeliner at the end of the day during her discussion with Jane in her office than earlier in the day while examining "Jessica" (or at possibly more eyeliner, although it looks like a different shade of brown).
Frankie says he wished teachers in Massachusetts had to submit fingerprints. It has been a requirement for employment of teachers in Massachusetts since January 2013..
In S3, E14, Frosts mother, says that she lives in Virginia.
In S5, E2, she arrives at BPD, requiring some comfort from the squad, again from somewhere reasonably close by, I.e. Virginia.
But after the funeral, when Jane gets home, she finds a postcard that has just arrived from Frost, and the postcard is from San Diego. More than a day of driving away.
In the beginning, a girl walks thru the lobby of the Police Station, carrying a gun and wearing a bloody blouse, all the way up to the floor where the detective division is & nobody sees her. No way.