Benjamin Franklin's mother, Abiah Folger, did not live in Salem. She was born and raised in Nantucket and moved to Boston when she was 21.
The ages of some of the people accused of being a witch are wrong. Martha Corey is portrayed to be about 50-60 and actually 70. Abigail Franklin looks to be in her 20s, but actually in her mid 30s and Samuel Wardwell looks to be 70 but was only in his 50s.
Flynn asks for a rifle. Rifles weren't invented until the 1800s. The weapon would have been a musket.