Tales of a Third Grade Nothing - S7-E6
Other mistake: In the cutaway at Ford's Theater, Abraham Lincoln receives a cell phone call from someone who is implied to be Thomas Jefferson. While the anachronism of a cell phone in the Civil War can be ignored as humorously deliberate, Lincoln can't be talking to Jefferson; by April of 1865, when Lincoln was assassinated, Jefferson had been dead for nearly 40 years.
Suggested correction: Where are you getting the implication that it is Thomas Jefferson? You seem to have misunderstood the joke. "I hear you took that black chick home. You're welcome." is not a reference to Jefferson sleeping with one of his slaves. It's simply a reference to Lincoln freeing the slaves. Tom is just a generic name. (Besides, if you're complaining about historical anachronisms in Family Guy cutaways, you're probably missing the point.)
The Man with Two Brians - S7-E5
Other mistake: Brian puts in a video tape of him as a puppy. But he hasn't been with the Griffins since he was a puppy. Peter picked him up from the street as a homeless adult dog.