When Matlock gets in the limo near the end, she is shown putting on her wedding ring. When she arrives at her house and hugs her grandson, she is not wearing the ring.
When Madeline introduces herself, she tells everyone "Yes, Matlock like the old TV show, which was all I heard between 1984 and 1992"; actually, the show Matlock (1986) was broadcast between 1986-1995. In the next episode Rome, in a Day (2024), Madeline realizes she made a blunder (the show did not end in 1992, but moved to ABC network, where it continued running for three more years) and explains that she does not count the ABC years, because the ratings went down, and it just didn't affect her as much. She does not, however, make an excuse regarding the blunder about the beginning year of the show.
When Madeline boards the bus, the fare shown is $2.75. The actual fare is $2.90, which has been in effect since August 2023. However, at the time the episode was filmed - a few YEARS before it aired - $2.75 was the correct fare. Furthermore, it is not established in what year the series takes place.
When Olympia leaves the first conference room with Matlock, she is shown first walking on carpet then hard floor, and her shoes make the same sound on both.
For Madeline to be hired by a New York law firm, they would have had to have checked her law license status through one of three official mechanisms, each of which is carefully managed by the state. This would have verified identity, address, current license status, disciplinary actions, etc. Madeline's deception about her true identity would have been exposed almost immediately.